PhysicsPhysics QuestionsWork, Energy And Power Questions for CBSE Class 11th

Work, Energy And Power Questions for CBSE Class 11th

  1. A body of mass m moving with a constant velocity v hits another body of the same mass moving with the same velocity v but in the opposite direction and sticks to it. The velocity of the compound body after collision is, if another body is at rest, then velocity of the compound body after collision is
  2. A body moves from rest with a constant acceleration. Which one of the following graphs represents the variation of its kinetic energy K with the distance travelled x ?
  3. The diagrams represent the potential energy U of a function of the inter-atomic distance r. Which diagram corresponds to stable molecules found in nature.
  4. A particle of mass m is moving in a horizontal circle of radius r under a centripetal force equal to − K / r 2 , where K is a constant. The total energy of the particle is
  5. A body of mass 2 kg moving with a velocity of 3 m/sec collides head on with a body of mass 1 kg moving in opposite direction with a velocity of 4 m/sec. After collision, two bodies stick together and move with a common velocity which in m/sec is equal to
  6. If g is the acceleration due to gravity on the earth’s surface, the gain in the potential energy of an object of mass m raised from the surface of earth to a height equal to the radius of the earth R, is
  7. Two particles of masses m 1 and m 2 in projectile motion have velocities v 1 and v 2 respectively at time t = 0. They collide at time t 0 . Their velocities become v 1 ‘ and v 2 ‘ at time 2 t 0 while still moving in air. The value of ( m 1 v 1 ‘   + m 2 v 2 ‘ ) − ( m 1 v 1   + m 2 v 2 ) is
  8. The adjoining diagram shows the velocity versus time plot for a particle. The work done by the force on the particle is positive from
  9. The potential energy function of a particle in the x-y plane is given by U=k(x+y) , where k is a constant . The work done by the conservative force in moving a particle from(1,1) to (2,3) is
  10. The speed v reached by a car of mass m in travelling a distance x, driven with constant power P, is given by
  11. A ball collides with a fixed inclined plane of inclination θ after falling through a distance h . If it moves horizontally just after the impact the coefficient of restitution is
  12. Two identical balls A and B are released from the position shown in the figure. They collide elastically with each other on the horizontal portion. The ratio of heights attained by A and B after collision is (neglect friction)
  13. Two identical cylindrical vessels with their bases at same level each contains a liquid of density ρ . The height of the liquid in one vessel is h 1 and that in the other vessel is h 2 . The area of either base is A. The work done by gravity in equalizing the levels when the two vessels are connected, is
  14. The potential energy of a weight less spring compressed by a distance a is proportional to
  15. Two solid rubber balls A and B having masses 200 and 400 gm respectively are moving in opposite directions with velocity of A equal to 0.3 m/s. After collision the two balls come to rest, then the velocity of B is
  16. A body of mass ‘M’ collides against a wall with a velocity v and retraces its path with the same speed. The change in momentum is (take initial direction of velocity as positive)
  17. A force F acting on an object varies with distance x as shown here. The force is in newton and x in metre. The work done by the force in moving the object from x = 0 to x = 6m is
  18. A particle of mass m moving with a velocity u makes an elastic one dimensional collision with a stationary particle of mass m establishing a contact with it for extremely small time T. Their force of contact increases from zero to F 0 linearly in time T 4 , remains constant for a further time T 2 and decreases linearly from F 0 to zero in further time T 4 as shown. The magnitude possessed by F 0 is
  19. A steel ball falls from a height h on a floor for which the coefficient of restitution is e. The height attained by the ball after two rebounds is
  20. A force F= 2i +3j- 4kN acts on a particle which is constrained to move in the XOY plane along the line x = y. If the particle moves 5 2 m, the work done by force in joule is
  21. A bob of mass M is suspended by an inextensible string. A particle of mass m, moving with velocity v 0 strike the bob as shown in the figure. The particle comes to rest just after collision. If θ = 30 ∘ , v o = 4 m / s and m M = 1 10 then calculate the velocity of the bob (in cm/s) just after collision.
  22. A heavy ball moving with speed v collides with a tiny ball at rest. The collision is elastic, then immediately after the impact, the second ball will move with a speed approximately equal to
  23. A simple pendulum of length l and mass m is initially at its lowest position . It is given the minimum horizontal speed necessary to move in a circular path about the point of suspension. The tension in the string at the lowest position of the bob is
  24. An engine pumps up 100 kg of water through a height of 10m in 5s. Given that the efficiency of the engine is 60%, What is the power of the engine ( Take g = 10 m s – 2 )
  25. A car moving with a speed of 50km/h can be stopped by brakes after at least 6m. If the same car is moving at a speed of 100km/h, the minimum stopping distance is
  26. A ball of mass m moving with speed u undergoes a head-on elastic collision with a ball of mass nm initially at rest. The fraction of incident energy transferred to the second ball is
  27. Two springs have their forces constant K 1 a n d K 2 and they are stretched to the same extension. if k 2 > k 1 work done is
  28. Two equal sphere A and B lie on a smooth horizontal circular groove at opposite ends of a diameter. At time t=0, A is projected along the groove and it first impinges on B at time t = T 1 and again at time t = T 2 If e is the coefficient of restitution, the ratio T 2 / T 1 is
  29. The bob of a simple pendulum is displaced from its equilibrium position O to a position Q which is at height h above O and the bob is then released. Assuming the mass of the bob to be m and time period of oscillations to be 2.0 sec, the tension in the string when the bob passes through O is
  30. A point mass of 1kg collides elastically with a stationary point mass of 5kg. After their collision, the 1kg mass reverses its direction and moves with a speed of 2m/s. Which of the following statement(s) is (are) correct for the system of these two masses? a) Total momentum of the system is 3kg m/s b) Momentum of 5kg mass after collision is 4kg m/s c) Kinetic energy of the centre of mass 1 2   total mass v c m 2 is 0.75 J d) Total kinetic energy of the system is 4J
  31. Three solid spheres each of mass m and radius R are placed at three corners of an equilateral triangle of side ‘d’ released. The speed of any one sphere at the time of collision would be d > 2 R [Assume there is no external gravitational force acting on the system of three spheres].
  32. A 15 g ball is shot from a spring gun whose spring has a force constant of 600 N/m. The spring is compressed by 5 cm. The greatest possible horizontal range of the ball for this compression is (g = 10 m/s 2 )
  33. A force acts on a 30g particle in such a way that the position of the particle as a function of time is given by x = 3 t − 4 t 2 + t 3 , where x is in metres and t is in seconds. The work done (in J) during the first 4 seconds is
  34. A force of 5 N, making an angle θ with the horizontal, acting on an object displaces it by 0 .4 m along the horizontal direction. If the object gains kinetic energy of 1J, the horizontal component of the force (in N) is
  35. If force and displacement of particle in direction of force are doubled. Work would become n times. The value of n is
  36. A body of mass 5 kg is placed at the origin, and can move only on the x-axis. A force of 10 N is acting on it in a direction making an angle of 60 o with the x-axis and displaces it along the x-axis by 4 metres. The work done (in J) by the force is
  37. A force F = ( 6 i ^ + 4 j ^ ) N acts on a body and produces a displacement S = ( 6 i ^ − 5 j ^ + 3 k ^ ) m . The work done will be (in J)
  38. A uniform chain of length 2 m is kept on a table such that a length of 60 cm hangs freely from the edge of the table. The total mass of the chain is 4 kg. What is the work done (in J) in pulling the entire chain on the table [ Take g = 10 m / s 2 ]
  39. A particle is acted upon by a force of constant magnitude which is always perpendicular to the velocity of the particle, the motion of the particle takes place in a plane. It follows that
  40. A ball of mass m moves with speed v and strikes a wall having infinite mass and it returns with same speed then the work done by the ball on the wall is
  41. A cord is used to lower vertically a block of mass M by a distance d with constant downward acceleration g 4 . Work done by the cord on the block is
  42. When a spring is stretched by 2 cm, it stores 100 J of energy. If it is stretched further by 2 cm, the stored energy will be increased by (in J)
  43. Natural length of a spring is 60 cm, and its spring constant is 4000 N/m. A mass of 20 kg is hung from it. The extension produced (in cm) in the spring is, (Take g = 9 .8   m / s 2 )
  44. The spring extends by x on loading, then energy stored by the spring is : (if T is the tension in spring and k is spring constant)
  45. A bomb of 12 kg explodes into two pieces of masses 4 kg and 8 kg. The velocity of 8kg mass is 6 m/sec. The kinetic energy of the other mass is
  46. Tripling the speed of the motor car multiplies the distance needed for stopping it by
  47. If a body looses half of its velocity on penetrating 3 cm in a wooden block, then how much will it penetrate more before coming to rest
  48. Two masses of 1 kg and 16 kg are moving with equal K.E. The ratio of magnitude of the linear momentum is
  49. An electric motor creates a tension of 4500 newton in a hoisting cable and reels it in at the rate of 2 m/sec. What is the power of electric motor
  50. A weight lifter lifts 300 kg from the ground to a height of 2 meter in 3 second. The average power generated by him is
  51. The power of a pump(in kW), which can pump 200kg of water to a height of 200m in 10sec is ( g = 10 m / s 2 )
  52. A car of mass 1250 kg is moving at 30m/s. Its engine delivers 30 kW while resistive force due to surface is 750N. What max acceleration can be given in the car
  53. From a waterfall, water is falling down at the rate of 100 kg/s on the blades of turbine. If the height of the fall is 100 m, then the power delivered to the turbine is approximately equal to
  54. From an automatic gun a man fires 360 bullet per minute with a speed of 360 km/hour. If each weighs 20 g, the power (in W) of the gun is
  55. A ball hits a vertical wall horizontally at 10 m/s bounces back at 10 m/s
  56. A body of mass m is at rest. Another body of same mass moving with velocity V makes head on elastic collision with the first body. After collision the first body starts to move with velocity
  57. An inelastic ball is dropped from a height of 100 m. Due to earth, 20% of its energy is lost. To what height the ball will rise
  58. A bag (mass M) hangs by a long thread and a bullet (mass m) comes horizontally with velocity v and gets caught in the bag. Then for the combined (bag + bullet) system
  59. A body of mass 2kg is moving with velocity 10 m/s towards east. Another body of same mass and same velocity moving towards north collides with former and coalesces and moves towards north-east. Its velocity is
  60. A lorry and a car moving with the same K.E. are brought to rest by applying the same retarding force, then
  61. The relation between the displacement X of an object produced by the application of the variable force F is represented by a graph shown in the figure. If the object undergoes a displacement from X = 0.5 m to X = 2.5 m the work done will be approximately equal to
  62. A particle which is constrained to move along the x-axis, is subjected to a force in the same direction which varies with the distance x of the particle from the origin as F ( x ) = − kx + ax 3 . Here k and a are positive constants. For x ≥ 0 , the functional from of the potential energy U ( x ) of the particle is
  63. The graph between E and 1 p is ( E = kinetic energy and p = momentum)
  64. The force acting on a body moving along x-axis varies with the position of the particle as shown in the fig. The body is in stable equilibrium at
  65. A particle is placed at the origin and a force F = kx is acting on it (where k is positive constant). If U ( 0 ) = 0 , the graph of U ( x ) versus x will be (where U is the potential energy function)
  66. A bullet of mass m moving with velocity v strikes a suspended wooden block of mass M and gets embedded in it. If the block rises to a height h, the initial velocity of the block will be
  67. There will be decrease in potential energy of the system, if work is done upon the system by
  68. If the error in the measurement of momentum of a particle is (+100%), then the error in the measurement of kinetic energy is
  69. A particle falls from a height h on a fixed horizontal plate and rebounds. If e is the coefficient of restitution, the total distance travelled by the particle before it stops rebounding is
  70. The work done by a force F = − 6 x 3 i ^ N in displacing a particle from x = 4 m to x = -2 m is
  71. under the action of a force, a 2 kg body moves such that its position x as a function of time is given by x= t 3 3 , where x is in metre and t is in second. The work done by the force in the first two seconds is
  72. A car of mass 500kg(including the mass of a block) is moving on a smooth road with velocity 1.0 m s – 1 along positive x-axis. Now a block of mass 25kg is thrown outside with absolute velocity of 20 m s – 1 along positive z-axis. The new velocity of the car is ( m s – 1 )
  73. In the figure m 1 and m 2 ( < m 1 ) are joined together by a pulley. When the mass m 1 is released from the height h above the floor , it strikes the floor with a speed
  74. A simple pendulum of length l and bob of mass m is displaced from its equilibrium position O to a position P so that height of P above O is h. It is then released. What is the tension in the string when the bob passes through the equilibrium position O? Neglect friction. V is the velocity of the bob at O
  75. An engine pumps water continuously through a hole. Speed with which water passes through the hole nozzle is v, and k is the mass per unit length of the water jet as it leaves the nozzle. Find the rate at which kinetic energy is being imparted to the water.
  76. A man places a chain (of mass m and length l) on a table slowly. Initially, the lower end of the chain just touches the table. The man brings down the chain by length l/2. Work done by the man in this process is
  77. A 500kg car ,moving with a velocity of 36 k m h – 1 on a straight road undirectionally, doubles its velocity in 1min. The average power delivered by the engine for doubling the velocity is
  78. A ball weight 1.0 kg is tied to a string 15cm long. Initially the ball is held in position such that the string is horizontal. The ball is now released .A nail N is situated vertically below the support at a distance L. The minimum value of L such that the string will be wound round the nail is
  79. A particular of mass ‘m’ moves along the quarter section of the circular path whose centre is at the origin. The radius of the circular path is ‘a’. A force F = y i ^ − x j ^ newton acts on the particle, where x,y denote the coordinates of position of the particle. Calculate the work done by this force in taking the particle from Point A (a,0) to Point B(0,a) along the circular path.
  80. A small sphere is given vertical velocity of magnitude v 0 = 5 m s – 1 and it swings in a vertical plane about the end of a massless string. The angle θ with the vertical at which string will break, knowing that it can withstand a maximum tension equal to twice the weight of the sphere, is
  81. Two pendulums each of length l are initially situated as shown in the figure. The first pendulum is released and strikes the second. Assume that the collision is completely inelastic and neglect the mass of the string and any frictional effects. How high does the centre of mass rise after the collision?
  82. A man is standing on a cart of mass double the mass of the man. Initially cart is at rest on the smooth ground. Now man jumps with relative velocity ‘v’ horizontally towards right with respect to cart. The work done by man during the process of jumping is
  83. The total work done on a particle is equal to the change in its kinetic energy
  84. The potential energy of a particle in force filed is U = A r 2 − B r where A and B are positive constants and ‘r’ is the distance of particle from the centre of the field . For stable equilibrium , the distance of the particle is
  85. If a spring extends by x on loading ,then energy stored by the spring is(if T is the tension in the spring and k is the spring constant)
  86. Which of the following is a non-conservative force?
  87. A body is tied at an end of a string of length ’l’ and rotated in a vertical circle. The string is just taut when the body is at the highest point.Velocity of the body when the string is in the horizontal position is
  88. Coefficient of restitution depends upon
  89. A molecule of mass m of an ideal gas collides with the wall of a vessel with a velocity v and returns back with the same velocity. The change in the linear momentum of the molecule is
  90. If the force acting on a body is inversely proportioned to its speed, then its kinetic energy is
  91. (A) : A bullet is fired from a gun which is initially at rest. Total K.E. is shared by the bullet and the gun in the inverse ratio of their masses. (R) : Linear momentum of the system is conserved.
  92. A bullet hits and gets embedded in a solid block resting on a frictionless surface. In this process which one of the following is correct?
  93. In order to cause a body to move along a circular path we must apply
  94. (A) comets move around the Sun in elliptical orbits. The gravitational force acting on the comet due to Sun is not normal to the comets velocity but the work done by the gravitational force over every complete orbit of the comet is zero. ( R) Gravitational Force is a non conservative force.
  95. (A) When a body slides on a rough surface, its momentum is not conserved. (B) When a ball falls from a height, momentum of earth, ball system is conserved (C) In case of explosion of flying bomb, momentum is conserved, in the presence of air
  96. (A) : Collision between two fundamental particles is elastic. (R) : Fundamental particles lose their shape in collision
  97. The area under a force – displacement curve gives
  98. The work done by gravity in lifting a body to a certain height does not depend depend upon
  99. When a wound spring is dissolved in an acid, the temperature of the acid
  100. If a curve is drawn expressing the K.E. of a particle as a function of the distance on x-axis. The slope of this curve represents the instantaneous
  101. A body is allowed to fall from a height ‘h’ above the ground. Then match the following. List – I List-II (a) P.E. = K.E. (e) at height h 2 (b) P.E. = 2K.E (f) constant at any point (c) K.E = 2P. E (g) at height of 2 h 3 (d) P.E. + K.E (h) at height of h 3
  102. A particle of mass M is moving in a circle of fixed radius ‘R’ in such a way that its centripetal acceleration at time ‘t’ is given by n 2 R t 2 . Where n is a constant, the power delivered to the particle by the force acting on it is
  103. A particle of mass m moving in the x-direction with speed 2v is hit by another particle of mass 2m moving in the y-direction with speed v. If the collision is perfectly inelastic, the percentage loss in the Energy during the collision is close to
  104. A spring of spring constant 5 × 10 3 N/m & stretched initially by 5 cm from the unstretched position. Then work done required to stretch it further by another 5cm is
  105. A Block of mass m = 0.1kg is connected to a spring of unknown spring constant k. It is compressed to a distance x from its equilibrium position and released from rest. After approaching the distance x 2 from equilibrium position , it hits another block and comes to rest momentarily, while the other block moves with a velocity 3m/s. The total initial Energy of the spring is,
  106. A uniform chain of length 2m is kept on a table, such that a length of 60 cm hangs freely from the edge of the table. The total mass of the chain is 4 kg. What is the work done in pulling the entire chain on the table ?
  107. A particle is moving in a straight line with retardation proportional to its displacement. Its loss of K.E for any displacement x is proportional to
  108. A body of mass 2kg is driven by an engine delivering a constant power of 1 J/s. The body starts from rest and moves in a straight line. After 9 seconds, the body has moved a distance (in m) .
  109. A bead of mass m can freely slide down the fixed inclined rod without friction. It is connected to a point P on the horizontal surface with a light spring of spring constant k. The bead is initially released from rest and the spring is initially unstressed and vertical. The bead just stops at the bottom of the inclined rod. Find the angle which the inclined rod makes with horizontal.
  110. Particle A collides elastically (perfect) with another particle B which was at rest. They disperse in opposite directions with same speeds. Ratio of their masses respectively must be
  111. A body with mass 2kg moves in one direction in the presence of a force which is described by the potential energy graph passing through (2,6) as shown. If the body is released from rest at x=2m, then it speed when it crosses x=5m is:
  112. For a particle rotating in a vertical circle with uniform speed, the maximum and minimum magnitudes of external force (other than gravity) acting on the particle are in the ratio 5:3. If the radius of vertical circle is 2m, the speed of revolving body (in m/s) is (take g = 10  m / s 2 )
  113. A body moves a distance of 10 m along a straight line under the action of a force of 5 N. If the work done is 25 joules, the angle which the force makes with the direction of motion of the body is
  114. Which of the following is a unit of energy
  115. It is easier to draw up a wooden block along an inclined plane than to haul it vertically, principally because
  116. A particle moves under the effect of a force F = Cx from x = 0 to x = x 1 . The work done in the process is
  117. A spring of force constant 10 N/m has an initial stretch 0.20 m. In changing the stretch to 0.25 m, the increase in potential energy is about
  118. Two springs have their force constant as k 1 and k 2 ( k 1 > k 2 ) . When they are stretched by the same force
  119. The force constant of a wire is k and that of another wire is 2k When both the wires are stretched through same distance, then the work done
  120. A body of mass 0.1 kg moving with a velocity of 10 m/s hits a spring (fixed at the other end) of force constant 1000 N/m and comes to rest after compressing the spring. The compression of the spring is ….(in m)
  121. The potential energy of a body is given by, U = A − Bx 2 (Where x is the displacement). The magnitude of force acting on the particle is
  122. The potential energy between two atoms in a molecule is given by U ( x ) = a x 12 − b x 6 ; where a and b are positive constants and x is the distance between the atoms. The atom is in stable equilibrium when
  123. When work is done on a body by an external force, its
  124. The bob of a simple pendulum (mass m and length l) dropped from a horizontal position strikes a block of the same mass elastically placed on a horizontal frictionless table. The K.E. of the block will be
  125. If the K.E. of a body is increased by 300%, its momentum will increase by (in %)
  126. If the linear momentum is increased by 50%, the kinetic energy will increase by (in %)
  127. The energy stored in wound watch spring is
  128. A car travelling at a speed of 30 km/hour is brought to a halt in 8 m by applying brakes. If the same car is travelling at 60 km/hour, it can be brought to a halt with the same braking force in
  129. In which case does the potential energy decrease
  130. Two bodies A and B having masses in the ratio of 3 : 1 possess the same kinetic energy. The ratio of their linear momenta is then
  131. Momentum of a particle is decreased by 20% without change in its mass. Find the percentage of change in its kinetic energy.
  132. A frictionless track ABCDE ends in a circular loop of radius R. A body slides down the track from point A which is at a height h = 5 cm. Maximum value of R for the body to successfully complete the loop is
  133. If the kinetic energy of a body becomes four times of its initial value, then new momentum will
  134. If the momentum of a body is increased by 100%, then the percentage increase in the kinetic energy is
  135. A particle of mass m at rest is acted upon by a force F for a time t. Its Kinetic energy after an interval t is
  136. Two identical blocks A and B, each of mass ‘m’ resting on smooth floor are connected by a light spring of natural length L and spring constant K, with the spring at its natural length. A third identical block ‘C’ (mass m) moving with a speed v along the line joining A and B collides with A. the maximum compression in the spring is
  137. The kinetic energy of a body of mass 3 kg and momentum 2 Ns is
  138. A 12 HP motor has to be operated 8 hours/day. How much will it cost at the rate of 50 paisa/kWh in 10 days (in Rs)
  139. A motor boat is travelling with a speed of 3.0 m/sec. If the force on it due to water flow is 500 N, the power of the boat
  140. An electric motor exerts a force of 40 N on a cable and pulls it by a distance of 30 m in one minute. The power supplied by the motor (in Watts) is
  141. Power of a water pump is 2 kW. If g = 10   m / sec 2 , the amount of water it can raise in one minute to a height of 10 m is (in litre)
  142. A truck of mass 30,000 kg moves up an inclined plane of slope 1 in 100 at a speed of 30 kmph. The power (kW)of the truck is (given g = 10 ms − 2 )
  143. A force of 2 i ^ + 3 j ^ + 4 k ^   N acts on a body for 4 second, produces a displacement of ( 3 i ^ + 4 j ^ + 5 k ^ ) m . The power used is
  144. An engine pump is used to pump a liquid of density ρ continuously through a pipe of cross-sectional area A. If the speed of flow of the liquid in the pipe is v, then the rate at which kinetic energy is being imparted to the liquid is
  145. If the heart pushes 1 cc of blood in one second under pressure 20000 N/m 2 the power (in W) of heart is
  146. A man does a given amount of work in 10 sec. Another man does the same amount of work in 20 sec. The ratio of the output power of first man to the second man is
  147. The principle of conservation of linear momentum can be strictly applied during a collision between two particles provided the time of impact is
  148. A sphere of mass m moving with a constant velocity u hits another stationary sphere of the same mass. If e is the coefficient of restitution, then the ratio of the velocity of two spheres after collision will be
  149. When two bodies collide elastically, then
  150. Two balls at same temperature collide. What is conserved
  151. A body falls on a surface of coefficient of restitution 0.6 from a height of 1 m. Then the body rebounds to a height of
  152. A ball is dropped from a height h. If the coefficient of restitution be e, then to what height will it rise after jumping twice from the ground
  153. A steel ball of radius 2 cm is at rest on a frictionless surface. Another ball of radius 4 cm moving at a velocity of 81 cm/sec collides elastically with first ball. After collision the smaller ball moves with speed of (cm/s)
  154. A body falling from a height of 10m rebounds from hard floor. If it loses 20% energy in the impact, then coefficient of restitution is
  155. When target is very light and at rest then after head on elastic collision it moves with double speed of projectile i.e. the velocity of body of mass m will be 2v.
  156. A tennis ball dropped from a height of 2 m rebounds only 1.5 m after hitting the ground. What fraction of its energy is lost in the impact
  157. A body of mass m moving with velocity v makes a head-on collision with another body of mass 2 m which is initially at rest. The loss of kinetic energy of the colliding body (mass m) is
  158. A tennis ball is released from height h above ground level. If the ball makes inelastic collision with the ground, to what height will it rise after third collision
  159. A mass ‘m’ moves with a velocity ‘v’ and collides inelastically with another identical mass. After collision the I st mass moves with velocity v 3 in a direction perpendicular to the initial direction of motion. Find the speed of the 2 nd mass after collision
  160. A body of mass m moving with a constant velocity v hits another body of the same mass moving with the same velocity v but in the opposite direction and sticks to it. The velocity of the compound body after collision is
  161. Two putty balls of equal mass moving with equal velocity in mutually perpendicular directions, stick together after collision. If the balls were initially moving with a velocity of 45 2   ms − 1 each, the velocity of their combined mass after collision is
  162. A moving body of mass m and velocity 3 km/h collides with a rest body of mass 2m and sticks to it. Now the combined mass starts to move. What will be the combined velocity (km/h)
  163. The displacement x of a particle moving in one dimension under the action of a constant force is related to the time t by the equation t = x + 3 , where x is in meters and t is in seconds. The work done (in J) by the force in the first 6 seconds is
  164. A force F = − K ( yi + xj ) (where K is a positive constant) acts on a particle moving in the xy-plane. Starting from the origin, the particle is taken along the positive x-axis to the point (a, 0) and then parallel to the y-axis to the point (a, a). The total work done by the force F on the particles is
  165. The kinetic energy acquired by a mass m in travelling a certain distance d starting from rest under the action of a constant force is directly proportional to
  166. Adjacent figure shows the force-displacement graph of a moving body, the work done in displacing body from x = 0 to x = 35   m is equal to
  167. A particle P moving with speed v undergoes a head -on elastic collision with another particle Q of identical mass but at rest. After the collision
  168. A toy car of mass 5 kg moves up a ramp under the influence of force F plotted against displacement x. The maximum height attained is given by
  169. The force required to stretch a spring varies with the distance as shown in the figure. If the experiment is performed with the above spring of half length, the line OA will
  170. Figure shows the F-x graph. Where F is the force applied and x is the distance covered by the body along a straight line path. Given that F is in newton and x in metre, what is the work done ?
  171. When a body moves with some friction on a surface
  172. A wooden block of mass M rests on a horizontal surface. A bullet of mass m moving in the horizontal direction strikes and gets embedded in it. The combined system covers a distance x on the surface. If the coefficient of friction between wood and the surface is μ , the speed of the bullet at the time of striking the block is (where m is mass of the bullet)
  173. A ball moving with speed v hits another identical ball at rest. The two balls stick together after collision. If specific heat of the material of the balls is S, the temperature rise resulting from the collision is
  174. A bag of sand of mass M is suspended by a string. A bullet of mass m is fired at it with velocity v and gets embedded into it. The loss of kinetic energy in this process is
  175. A rifle bullet loses 1/20 th of its velocity in passing through a plank. The least number of such planks required just to stop the bullet is
  176. Two blocks of masses m 1 and m 2 connected by a non-deformed light spring rest on a rough ground as shown in figure. If friction coefficient on ground is μ then find the minimum constant force F to be applied on m 2 so that m 1 start sliding.
  177. A force F = ( 3 xy − 5 z ) j ^ + 4 z k ^ is applied on a particle. The work done by the force when the particle moves from point (0, 0, 0) to point (2, 4, 0) as shown in figure is
  178. A 500-kg car, moving with a velocity of 36 kmh -1 on a straight road unidirectionally, doubles its velocity in 1 min. The average power delivered by the engine for doubling the velocity is
  179. In figure, the variation of potential energy of a particle of mass m = 2 kg is represented w.r.t its x-coordinate. The particle moves under the effect of the conservative force along the x-axis. Which of the following statements is incorrect about the particle?
  180. The potential energy of diatomic molecule is given by U = A r 12 – B r 6 where, r is the distance between the atoms that make up the molecule and A and B are positive constants. Find the equilibrium separation between the atoms.
  181. A spring of spring constant 5× 10 3 N/m is stretched initially by 5cm from the unstretched position. The work required to further stretch the spring by another 5cm is
  182. A spring of spring constant 5× 10 3 N/m is stretched initially by 5cm from the unstretched position. The work required to further stretch the spring by another 5cm is
  183. under the action of a force, a 2 kg body moves such that its position x as a function of time is given by x= t 3 3 , where x is in metre and t is in second. The work done by the force in the first two seconds is
  184. A body has a kinetic energy E when projected at an angle of projection for maximum range. Its kinetic energy at its highest point of its path will be
  185. A car of mass m is accelerating on a level smooth road under the action of a single force F. The power delivered to the car is constant and equal to P. If the velocity of the car at an instant is v, then after travelling how much distance it becomes double?
  186. An ideal massless spring S can be compressed 1 m by a force of 100N in equilibrium .The same spring is placed at the bottom of a frictionless inclined plane at 30 o to the horizontal. A 10kg block M is releases from rest at the top of the incline and is brought to rest momentarily after compressing the spring by 2m. If g = 10 m s – 2 , what is the speed of mass just before it touches the spring?
  187. The given plot shows the variation of U, the potential energy of interaction between two particles with the distance separating them r. 1. B and D are equilibrium points 2. C is the point of stable equilibrium 3. The force of interaction between two particles is attractive between points C and D are repulsive between D and E 4. The force of interaction between particles is repulsive between points E and F. Which of the above statement are correct?
  188. A block of mass 1 kg slides down a curved track which forms one quadrant of a circle of radius 1m as shown in figure. The speed of block at the bottom of the track is v= 2 m s – 1 . The work done by the force of friction is (g=10m/ s 2 )
  189. A bead of mass 1 2 kg starts from rest from A to move in vertical plane along a smooth fixed quarter ring of radius 5m , under the action of a constant horizontal force F = 5N as shown.The speed of bead as it reaches the point B is [Take g = 10 m s – 2 ]
  190. The potential energy function for a diatomic molecule is U(x) = a x 12 − b x 6 . In stable equilibrium , the distance between the particles is
  191. A particle is projected at t=0 from a point on the ground with certain velocity at an angle with the horizontal. The power of gravitation force is plotted against time. Which of the following is the best representation?
  192. Three identical particle with velocities v 0 i ^ , − 3 v 0 j ^ and 5 v 0 k ^ collide successively with each other in such a way that they form a single particle. The velocity vector of resultant particle is
  193. A steel ball is dropped on a hard surface from a height of 1 m and rebounds to a height of 64 cm. The maximum height attained by the ball after n t h bounce is (in m)
  194. A block of mass 10kg is moving in x direction with a constant speed of 10m/s. It is subjected to a retarding force F=-0.1xJ/m during its travel from x=20m to x=30m. Its final kinetic energy will be
  195. A massless platform is kept on a light elastic spring as shown in the figure. When a particle of mass 0.1 kg is dropped on the pan from a height of 0.24m, the particle strikes the pan and the spring is compressed by 0.01m. From what height should the particle be dropped to cause a compression of0.04m?
  196. A particle located in a one-dimensional potential field has its potential energy function as U(x)= a x 4 − b x 2 ,where a and b are positive constants. The position of equilibrium x corresponds to
  197. A person of mass 70kg jumps from a stationery helicopter with the parachute open .As he falls through 50m height, he gains a speed of 20 m s – 1 . .The work done by the viscous air drag is
  198. The block of mass M moving on a frictionless horizontal surface collides with a spring of spring constant k and compresses it by length L. The maximum momentum of the block after collision is
  199. A stationery body of mass 3kg explodes into three equal pieces. Two of the pieces fly off at right angles to each Other. One with a velocity of 2 i ^ m/s and other with a velocity of 3 i ^ m/s.If the explosion takes place in 10 – 5 s, the average force acting on the third piece in newtons is
  200. A particle of mass 100g is thrown vertically upward with a speed of 5m/s. The work done by the force of gravity during the time the particle goes up is
  201. Figure show the vertical section of a frictionless surface. A block of mass 2kg is released from rest from position A; its KE as it reaches position C is ( g = 10 m s – 2 )
  202. Two identical bodies of same mass are raised to same heights by two persons X and Y in 10s and 20s respectively . The work done by
  203. A bead of mass ½ kg starts form rest from A to move in a vertical plane along a smooth fixed quarter ring of radius 5 m, under the action of a constant horizontal force F= 5N as shown in the figure. The speed of bead as it reaches point B is
  204. The area under a ‘force – displacement’ curve gives
  205. The work done by the external forces on a system equals the change in
  206. A body is moving undirectionally under the influence of a source of constant power supplying energy . Which of the diagrams shown below correctly shows the displacement time curve for its motion?
  207. A body is initially at rest. It under goes one-dimension motion with constant acceleration. The power delivered to it at time t is proportional to
  208. The potential energy of a system increases if work is done
  209. A boy carrying a box on his head is walking on a level road from one place to another on a straight road is doing no work. The statement is
  210. A particle with the total energy E is moving in a potential energy region U(x). Motion of the particle is restricted to the region when
  211. A bullet hits a block at rest on a frictionless horizontal surface and get embedded into it. The physical quantity associated with the block that remains unchanged is
  212. Which of the following is an example of completely Inelastic collision
  213. When a ball hits a floor and rebounds after an inelastic collision,
  214. A ball of mass ‘m’ is rotated in a vertical circle with constant speed. The difference in tension at the top and bottom would be
  215. Sand is falling on a conveyor belt at the rate of 5 k g s – 1 . The extra power required to move the belt with a velocity of 6 m s – 1 is,
  216. The velocity of a body revolving in a vertical circle of radius ‘r’ at the lowest point 7 g r . The ratio of maximum to minimum tensions in the string is
  217. Which of the following statement is wrong ?
  218. A rock of mass m is dropped to the ground from a height h. A second rock with mass 2m is dropped from the same height. When second rock strikes, the ground, what is its K.E.?
  219. A particle is acted upon by a force of constant magnitude, which is always perpendicular to the velocity of the particle, the motion of the particle takes place in a plane. It follows that
  220. If a machine is lubricated with oil, then
  221. A sphere ‘A’ moving with a speed ‘u’ and rotating with angular velocity ‘w’ makes head-on elastic collision with an identical stationery sphere ‘B’. There is no friction between the surface ‘A’ and B, neglect gravity (a) ‘A’ will stop moving but continue to rotate with angular velocity ‘W’ (b) ‘B’ will move with speed ‘u’ without rotating. (c) ‘B’will move with speed ‘u’ and rotate with an angular velocity ‘W’ (d) ‘A’ will come to rest and stop rotating.
  222. (A) For any collision, momentum transfer takes place (B) In any collision, Energy transfer takes place (C) Impulsive forces are involved in collisions.
  223. (A) Collision doesn’t require physical contact. (B) Collision between sub atomic particles is elastic. (C) Collision between macroscopic bodies is generally ineleastic.
  224. A man is waiting at a bus stop by holding a box on his head. Work done by him is
  225. In case of a conservative force
  226. Velocity –time graph for a Body of mass 10kg is shown in figure. Work done on the Body in first two seconds of the motion is
  227. A car of weight w is on inclined road, that rises by 100m over a distance of 1km and applies a constant frictional force w 20 on the car. While moving uphill on the road at a speed of 10 m/s , the car needs power p. If it needs power p 2 while moving downhill at speed v, then value of v is
  228. A person trying to loose weight by burning fat lifts a mass of 10kg up to a height of 1m 1000 times. Assume that the P.E. lost each time he lowers the mass is dissipated. How much mass of fat will be use up considering the work done only when the weight is converted to mechanical energy with a 20% efficiency rate. Take g    =     9.8   m / s 2 ; Energy of fat per unit mass = 3.8   ×    10 7   J / k g
  229. A particle is moving in a circle of radius ‘r’ under the action of a force F   =    α r 2 , which is directed towards centre of the circle. Total mechanical energy of the particle is (take P.E. = 0 at r = 0)
  230. A Body is moved along a straight line by a machine delivering a constant power. The distance moved by the Body in time ‘t’ is proportional to
  231. A spring of force constant 800 N/m has an extension of 5 cm. The work done in extending it from 5cm to 15cm is,
  232. A body of mass m, accelerates uniformly from rest to V 1 in time t 1 . The instantaneous power delivered to the Body as a function of time ‘t’ is
  233. The block of mass M moving on the friction less horizontal surface, collides with the spring of the spring constant K and compresses it by length L. The maximum momentum of the block after collision is
  234. A force F ¯    =    ( 5 i ∧ + 3 j ∧ + 2 k ∧ )   N is applied over a particle which displaces it from its origin to the point r ¯    =    ( 2 i ∧ − j ∧ )   m . The work done on the particle in Joules is
  235. A body of mass M is accelerated uniformly from rest to a speed V in time T. The instantaneous power delivered to the body as a function of time is given by
  236. A Bomb of mass 16kg at rest explodes into two pieces of masses 4kg & 12kg. The velocity of the mass 12kg is 4 m/s. The K.E. of the other mass is
  237. A mass of M kg is suspended by a weight less string the horizontal force that requires to displace it until the string making an angle 45° with the initial vertical direction is
  238. A particle of mass 100 gm thrown vertically upwards with a speed of 5 m/s. The work done by the force of gravity during the time, the particle goes up is
  239. A 2kg Block slides on a horizontal floor with speed of 4 m/s. It strikes a uncompressed spring and compresses it till the block is motionless. The kinetic friction force is 15N and spring constant is 10,000 N/m. The spring compressed by
  240. The potential energy of a 1 kg particle free to move along the x-axis is given by V ( x )    =      x 4 4 − x 2 2 Joules. The total Mechanical Energy of the particle 2J. Then the maximum speed is,
  241. When a Rubber Band is stretched by a distance x, it exerts a restoring fore of magnitude F    =      a x + b x 2 where a and b are constants. The work done in stretching the unstretched rubber band by L − is
  242. A block of mass 0.5 kg is moving with speed of 2 m/s on a smooth surface. It strikes another mass of 1 kg and then they move together as a single body. The Energy loss during the Collision is,
  243. A particle strikes a horizontal friction less floor with a speed u, at an angle θ   , with the vertical and rebounds with a speed V, at an angle α with vertical . Find the value of V if e is the coefficient of restitution.
  244. A sphere A of mass m moving with certain velocity hits another stationery sphere B of different mass. If the ratio of velocities of the spheres after collision is V A V B     =     1 − e 1 + e , where ‘e’ is coefficient of restitution. The initial velocity of sphere A with which it strikes is,
  245. A particle of mass ‘m’ moving with a velocity 3 i ∧ + 2 j ∧ m/s, collides with a stationary mass ‘M’ and finally m moves with velocity − 2 i ∧ + j ∧ m/s. If m M   =    1 13 , the velocity of the M after collision is,
  246. A particle is moving with kinetic Energy E, straight up an inclined plane with an angle α , the coefficient of friction being μ . The work done against friction before the particle comes to rest is,
  247. Two particles of masses m 1    a n d    m 2 repel each other by a force F     =      C r 2 , where C is a constant and r the separation between m 1    a n d    m 2 mass m 1 is fixed and m 2 is released from rest from on initial separation r i from m 1 . Speed of m 2 when it is at extremely large distance from m 1 , while moving away from m 1 is ,
  248. A mass 10kg moving with a speed 10 cm/s on a smooth horizontal surface hits a spring as shown in figure. Work done by the spring force on the mass is ,
  249. An Electric pump is used to fill an overhead tank of capacity 9 m 3 kept at a height 10 m above ground. If the pump takes 5 minutes to fill the tank by consuming 10 kilo watt power, efficiency of the pump should be ( t a k e    g    =     10 m / s 2 )   
  250. A Bullet when fired at a target has its velocity decreased to 50% after penetrating 30 cm into it. Additional thickness it will penetrate in cm before coming to rest is,
  251. An object of mass 4 kg is moving along x-axis such that its position x- varies with time ‘t’ as x 2   =   16 t 3 , with x in metre and t in sec. Work done as a function of time can be shown as
  252. A spring of force constant K is cut into two pieces such that one piece is double the length of other. Then the long piece will have a force constant of
  253. A human heart pumps 60 cc of blood through the arteries at each beat against an average pressure 10 cm of mercury. If the pulse beats 72 times in a minute, the pumping power of heart will be nearly(Density of mercury = 13.6 gm/cc, g     =     10 c m / s 2 )
  254. An object of mass 6 kg is moved with uniform speed of 8 m/s for 8 sec on a surface. Co efficient of friction between the body and the surface is 0.6 , work done for a given motion of the body is ( t a k e     g    =     10 m / s 2 )
  255. An object of mass 2 kg is placed at rest on a frictionless horizontal surface. A horizontal force is given by F ¯    =      ( x 2 − 9 ) ℓ ∧   N acts on it along x-axis. Kinetic energy of the object will be maximum at
  256. A particle of mass ‘M’ moved under a constant power Po. At same instant after the start, its speed is V and at a later instant, the speed is 2V; Neglecting friction, distance travelled by the particle as its speed increases from V to 2V is
  257. A body is moving along a straight line under a force that delivers constant power. Distance travelled by the body in time ‘t’ is proportional to
  258. The P.E of a conservative system is given by V ​ ( x )    =     ( x 2 − 3 x )   J , where x is measured in metre. Then its equilibrium position is at
  259. A bullet of mass ‘m’ is fired with certain velocity from a gun of mass M. Gun, which is attached with one end of the spring compresses by distance ‘d’. If ‘K’ is the spring constant K, velocity of the bullet is
  260. N m s − 1 i s t h e u n i t o f
  261. A 60 HP electric motor lifts an elevator having a maximum total load capacity of 2000 kg. If the frictional force on the elevator is 4000N, the speed of the elevator at full load is close to: 1 H P = 746 W , g = 10 m s − 2
  262. An elevator in a building can carry a maximum of 10 persons, with the average mass of each person being 68 kg. The mass of the elevator itself is 920 kg and it moves with a constant speed of 3m/s. The frictional force opposing the motion is 6000N. If the elevator is moving up with its full capacity, the power delivered by the motor to the elevator (g = 10 m/ s 2 ) must be at least ;
  263. A body A, of mass m= 0.1kg has an initial velocity of 3 i ∧ m s − 1 . It collides elastically with another body, B of the same mass which has an initial velocity of 5 j ∧ m s − 1 . After collision, A moves with a velocity v = 4 i ∧ + j ∧ . The energy of B after collision is written as x 10 J . the value of x is
  264. Two particles of equal mass m have respective initial velocities u i ^ and u i ^ + j ^ 2 . They collide completely inelastically. The energy lost in the process is :
  265. Consider a force F = − x i ^ + y j ^ . The work done by this force in moving a particle from point A 1 , 0 to B 0 , 1 along the line segment is (all quantities are in SI units)
  266. A particle of mass m is projected with a speed u from the ground at angle θ = π 3 w.r.t. horizontal ( x-axis). When it has reached its maximum height, it collides completely inelastically with another particle of the same mass and velocity u i ^ . The horizontal distance covered by the combined mass before reaching the ground is
  267. A particle of mass m with an initial velocity u i ^ collides perfectly elastically with a mass 3m at rest. It moves with a velocity v j ^ after collision, then, v is given by:
  268. A particle of mass m is moving along the x-axis with initial velocity u i ^ . It collides elastically with a particle of mass 10m at rest and then moves with half its initial kinetic energy, (see figure). If sin θ 1 = n sin θ 2 then value of n is
  269. A cricket ball of mass 0.15 kg is thrown vertically up by a bowling machine so that it rises to a maximum height of 20 m after leaving the machine. If the part pushing the ball applies a constant force F on the ball and moves horizontally a distance of 0.2 m while launching the ball, the value of F (in N) is g = 10 m s − 2
  270. A particle is moving unidirectionally on a horizontal plane under the action of a constant power supplying energy source. The displacement (s) – time (t) graph that describes the motion of the particle is (graphs are drawn schematically and are not to scale) :
  271. A block of mass 1.9 kg is at rest at the edge of a table, of height 1m. A bullet of mass 0.1kg collides with the block and sticks to it. If the velocity of the bullet is 20m/s in the horizontal direction just before the collision then the kinetic energy just before the combined system strikes the floor, is [Take g = 10m/ s 2 . Assume there is no rotational motion and loss of energy after the collision is negligible]
  272. A block starts moving up an inclined plane of inclination 30 0 with an initial velocity of v 0 . It comes back to its initial position with velocity v 0 2 . The value of the coefficient of kinetic friction between the block and the inclined plane is close to I 1000 . The nearest integer to I is
  273. Blocks of masses m, 2m, 4m and 8m are arranged in a line on a frictionless floor. Another block of mass m, moving with speed v along the same line (see figure) collides with mass m in perfectly inelastic manner. All the subsequent collisions are also perfectly inelastic. By the time the last block of mass 8m starts moving the total energy loss is p% of the original energy. Value of ‘p’ is close to :
  274. A person pushes a box on a rough horizontal plateform surface. He applies a force of 200 N over a distance of 15 m. Thereafter, he gets progressively tired and his applied force reduces linearly with distance to 100 N. The total distance through which the box has been moved is 30 m. What is the work done by the person during the total movement of the box?
  275. Two identical cylindrical vessels are kept on the ground and each contain the same liquid of density d. The area of the base of both vessels is S but the height of liquid in one vessel is x 1 and in the other, x 2 . When both cylinders are connected through a pipe of negligible volume very close to the bottom, the liquid flows from one vessel to the other until it comes to equilibrium at a new height. The change in energy of the system in the process is
  276. A particle which is experiencing a force given by F = 3 i ^ − 12 j ^ undergoes a displacement of d = 4 i ^ . If the particle had a kinetic energy of 3 J at the beginning of the displacement , what is the kinetic energy at the end of the displacement?
  277. Force acting on a particle moving in a straight line varies with velocity of the particle as F = k v , k is a constant. The work done by this force in time t is : (At t=0, particle is moving with non zero speed)
  278. Figure shows a body of mass M sliding from rest down a frictionless fixed track of radius R in time t. Assume that the body started from the top of the track A and slides to the bottom B. The change in the magnitude of gravitational potential energy is
  279. System shown in figure is released from rest with the spring at natural length. Pulley and spring is massless and friction is absent everywhere. The speed (in m/s) of 5kg block when 2kg block leaves the contact with ground is (Take force constant of spring k = 40 N / m and g = 10 m / s 2 , 2 = 1.414 )
  280. A small ball moves towards right with a velocity v starting from A. It collides with the wall and returns back and continues to and fro motion. If the average speed for the first trip is (2/3)v, the coefficient of restitution of impact (in 10 -1 ) is .
  281. The work done by a force F = 2 ( x + 4 y ) i ^ + 8 x j ^ N on a particle moving from origin to (4 m, 2 m, 0) along the path x 2 = 8y is 10 × n J. The value of n is
  282. As part of his discovery of the neutron in 1932, James Chadwick determined the mass of the neutron (newly identified particle) by firing a beam of fast neutrons all having the same speed, as two different targets and measuring the maximum recoil speeds of the target nuclei. The maximum speed arises when an elastic head-on collision occurs between a neutron and a stationary target nucleus. Represent the masses and final speeds of the two target nuclei as m 1 , v 1 , m 2 and v 2 and assume Newtonian mechanics applies. The neutron mass can be calculated from the equation m n = m 1 v 1 − m 2 v 2 v 2 − v 1 Chadwick directed a beam of neutrons on paraffin, which contains hydrogen. The maximum speed of the protons ejected was found to be 3.3 × 10 7 m / s A second experiment was performed using neutrons from the same source and nitrogen nuclei as the target. The maximum recoil speed of the nitrogen nuclei was found to be 4.7 × 10 6 m / s . The masses of a proton and a nitrogen were taken as 1 u and 14u, respectively. What was Chadwick’s value for the neutron mass?
  283. A chicken is scratching the ground. The work done by it on the dirt is
  284. A person travels certain distance on a rough horizontal surface. Work done by frictional force is
  285. The work done by conservative force is
  286. A graph is drawn by taking force along Y-axis and displacement along X-axis. The work done by the force is given by
  287. A body is projected vertically upwards such that it reaches maximum height ‘h’. The total work done by gravitational force during its flight is
  288. A body is taken from A to B along three paths under the action of a conservation force. If W 1 ,W 2 &W 3 are work done along the three paths, then
  289. A body is dropped from certain height. The work done by gravity is
  290. A spring of force constant ‘K’ is stretched by a force ‘F’. The energy stored in the spring is
  291. A force of 100N is acting on a 10kg block at 60 o above the horizontal. If it travels 5m in 10s work done by force is
  292. A force F = ( 4 i − 3 j + 7 k ) N moves a particle from ( i ^ + j ^ + k ^ ) m to 2 i ^ + 3 j ^ − 5 k ^ ​​  m . The work done by the force is
  293. A motor cycle comes to a skidding stop in 5m.If force applied by the road on the motor cycle is 500N. Calculate the (i) work done by the road on the motor cycle (ii) work done by the motor cycle on the road
  294. A particle of mass 1kg is displaced from(0,0,0) to (2m,2m,2m) under the action of a force ( 9 i ^ + 4 j ^ ) N .The work done by the force is
  295. Three forces ( 5 i ^ + 4 j ^ + 2 k ^ ) N     ( − 2 i ^ − 2 j ^ + 6 k ^ ) N , ( i ^ − j − 3 k ^ ) N displaces a particle from (1m,-1m,-1m) to (1m,0,3m) and then to (3m,1m,2m). The total work done by all these forces is
  296. A force of 20 2 is acting on a block of 1kg at 45 ∘ above the horizontal. Work done by all the forces in 2s is (g= 10 m s − 2 )
  297. A force of 10N acts on a body of mass 5kg at rest. The work done in 4 th second is
  298. A particle is displaced from a position vector 4 i ^ + 2 j ^ m to 2 i ^ + 3 k ^ m by applying a force of f = 3 x 2 i ^ + 2 y j ^ N . The work done is
  299. The displacement of a body of mass 10kg moving on a smooth horizontal surface is given by s = t 4 4 . The work done in first 2 seconds is
  300. A particle is displaced from (1m,1m,1m) to (2m,2m,2m) under a force F = ( 2 x y i ^ + x 2 j ^ ) N . The work done by this force is
  301. A force of F=(3+5 x ) i ^ N displaces a particle from (1,0,0)m to (3,5,-2) m. The work done is
  302. A body of mass 2 kg at rest acquires a velocity of 10ms -1 in 4 seconds. The work done is
  303. The work done by a force of ( 2 x i ^ + 30 j ^ ) N in displacing the particle from (1,0,2) m to (2,y,2) m is zero. The value of y is
  304. A force F = 2 t i + 5 t 2 j ^ N acts on a body due to which displacement varies as S = 3 t 2 i ^ + 4 k ^ m work done in 3 seconds is
  305. A particle is subjected to a force which varies with displacement as shown in figure. The total work done is
  306. Force acting on a particle varies with displacement as shown in figure. The work done from x=-4m to x=+4m is
  307. A 4kg block is acted upon by force as shown in figure. The work done by the force from x=0 to x=8m is
  308. Find the work done at the end of displacement 60cm in the graph shown.
  309. The relationship between the force F and position of a body is as shown in figure. The work done in displacing the body from x=1m to x=4m is
  310. A conservative force F = ( − a x + b x 2 ) i ^ is acting on a particle where a ,b are constants. The change in potential energy when particle is displaced from x=3m to x=4m (Take U=0 at x=0)
  311. The potential energy of a conservative system is given by U= ( 10 x 2 − 4 X ) J .The equilibrium position is
  312. The potential energy of a configuration is expressed as U(x,y)= 5 x 2 y . The force acting the particle at (1m,1m,1m) is
  313. A box of mass 5kg is kept on a rough horizontal surface. The coefficient of friction between box and surface is 0.5. The work done by kinetic friction in moving the box from A to B and back to A (AB=2m)
  314. A conservative force is given by the function F = K r 2 , K is a constant. If potential energy is zero at r = r 0 , then potential energy at r = ∞ is
  315. A uniform rod of mass 3 kg and length 2m is lying on a horizontal surface. It is raised until it makes an angle 30 ∘ with vertical. The work done by gravity is (g=9.8ms -2 )
  316. The potential energy of a force field is given by U = sin ( x + y ) . The force acting on the particle at position π 4 , π 4 is
  317. The potential energy of a conservative force field is given by U = 3 x 2 y − 6 z .The force acting on particle is
  318. A force 100N produces an elongation of 20cm in a spring. The work done against spring force is
  319. A 2kg block is pulled upwards by 60N force. The ratio of magnitudes of total work done and work done against gravity after 3 seconds (g=10ms − 2 )
  320. A body of mass m is placed on the top of inclined plane of inclination θ and length l the work done by gravity when it reaches the bottom of inclined plane is
  321. A simple pendulum of length 1m having bob of mass 100g is displaced through 60 ∘ from equilibrium position. The work done by gravity is ( g = 10 m s − 2 )
  322. The work done in stretching a spring through 2cm is 10J. The work done in stretching the spring further through 6cm is
  323. A spring of force constant 150 Nm − 1 is stretched through 10cm. The energy stored in the spring is
  324. A block attached to a spring pulled by a constant horizontal force is kept on a smooth horizontal surface as shown in figure. The maximum work done by applied force ‘F’, if initially spring is in its natural state
  325. When a spring is compressed by 3cm, the potential energy stored in it is U. When it is compressed further by 3cm, the percentage increase in potential energy is
  326. A ladder of mass 10kg is lying on horizontal surface. A body of weight 200N is attached to one end of ladder. If length is 5m and its centre of mass is at a distance of 2m from one end, the total work done in lifting the ladder to vertical position is
  327. A block of mass 2Kg is attached to the lower end of a spring of force constant 1960 N m − 1 hanging from rigid support. Initially spring is unstretched, if the block is suddenly released the maximum elongation produced in spring is
  328. A block of mass 10kg is kept on an inclined plane of inclination 30 ∘ . If the inclined plane is moving upwards with acceleration of 2ms -2 and the block does not slide on the plane, work done by gravity in 3 seconds is g=9.8ms − 2
  329. A system consisting of two blocks of masses m 1 and m 2 connected by a spring of spring constant K. A force F is applied on m 1 along its weight and removed such that m 2 is just lifted. Then F is
  330. A body of 5kg has linear momentum 20 k g m s − 1 its kinetic energy is
  331. A bucket filled with water weighing 30kg is raised from a well of depth 10m. If the linear density of rope is 0.2kg per meter, the amount of work done is ( g = 10 ms − 2 )
  332. A block of mass ‘m’ sliding on a smooth horizontal surface with a velocity ‘v’ meets a long horizontal spring fixed at one end and having spring constant k as shown in figure. The maximum compression of the spring is
  333. A body of mass 2kg at rest is acted on by two mutually perpendicular forces 6N and 8N simultaneously. Its kinetic energy after 10s is
  334. A river is flowing with a velocity of 4 m s − 1 . If density of water is 1 g c m − 3 , the kinetic energy of each cubic meter of water is
  335. A body is projected vertically downwards with an initial velocity from a height of 10m on to a horizontal floor. During the impact it losses 50% of its energy and rebounds to the same height. The velocity of projection is   ( g = 9.8 m s − 2 )
  336. A particle moves in a straight line with retardation proportional to its displacement. Its loss of kinetic energy for any displacement ‘x’ is proportional to
  337. A body moving with velocity of 10 m s − 1 has linear momentum 5Ns. Its kinetic energy is
  338. If the kinetic energy of a body increases by 125% the percentage change in momentum is
  339. In case of freely falling body, the ratio of KE of the body at the end of 4 th second to increase in KE in the next four seconds is
  340. The displacement of a particle of mass 2kg varies with time as S = 2 t 2 − 2 t + 10 m . The change in kinetic energy of the particle in a time interval t=0 to t=2s is
  341. A particle of mass 0.5kg is moving in X-Y plane whose position at an instant ‘x’ is r = 4 sin 2 t i ^ + 4 ( 1 − cos 2 t ) j ^ m, where r is in metre and t is second. The kinetic energy of the particle at an instant ‘t’ is
  342. The kinetic energy of a man is half of that of a boy whose mass is half of that of man. When the man speeds up by 5ms -1 , his kinetic energy is 100% more than that of the boy. The initial velocity of man is
  343. A ball of mass 100g is projected upward with an initial velocity 10 m s − 1 and comes back and finally achieved a velocity of 5 m s − 1 at the point of projection. The work done by air resistance
  344. A bullet moving with a speed of 150 m s − 1 can just penetrate into two planks of equal thickness. Then the number of such planks required, if speed is tripled will be
  345. A block is released from rest from a height of 10m. After travelling through the smooth surface it moves on the rough surface horizontal surface through a length of 6m and climbs on to the other smooth curved surface through a height h ‘ .If μ = 0.5 then h ‘ =
  346. The velocity of a body of mass 3kg is increased from 10 m s − 1 to 14 m s − 1 under the influence of external force. The network done by external force is
  347. A block of mass 10kg slides down from the top of an inclined plane of length 3m. The first 1m of the plane is smooth and next 2m is rough. The block is released from rest from top of the plane and again comes to rest at the bottom of the plane. If the angle of inclination of plane is 30 ∘ , the coefficient of friction between plane and block on rough portion is
  348. A 10kg body moves along X-axis from x = 0 to x = 5 m under the influence of a force given by F = 5 − 2 x + 3 x 2 . If the body starts from rest, the velocity at x = 5 m is
  349. A particle of mass ‘m’ is projected at 60 ∘ to vertical with an initial velocity ‘u’ . The work done by gravity during the time it reaches maximum height is
  350. A helicopter lifts a 60kg astronaut 15m vertically from the ocean by means of a cable. The acceleration of astronaut is g 10 m s − 2 . What is the speed of astronaut just before he reaches the helicopter ( g = 9.8 m s − 2 )
  351. A simple pendulum has a length 1m. The mass of bob is 100g. If it is displaced through 60 ∘ from equilibrium, the potential energy of bob in this position is
  352. A 10 kg body is dropped from a height of 20m. After hitting ground it rises to 15m. The loss in potential energy is
  353. A rectangular block of dimensions 8m × 4m × 2m and of density 1.5 g c m − 3 is lying on horizontal ground. The ratio of maximum to minimum potential energies is
  354. A 2kg body is projected vertically upwards with a velocity of 100 m s − 1 from ground .The ratio of potential energies 4s and 2s after projection is g = 10 m s − 2
  355. Twenty identical cubical blocks each of mass 100g and of side 10cm are placed one above the other. The potential energy of 15 th block from bottom is g = 10 m s − 2
  356. A smooth chain of mass m rests against a surface in the form of a quarter of circle of radius ‘r’. If it is released from, the velocity of chain after it cmes over the horizontal part of the surface is
  357. A uniform meter scale of mass 2kg is suspended from one end. If it is displaced through an angle 60 ∘ from the vertical, the increase in potential energy is
  358. A man slowly pulls a bucket of water from a well of depth h=20m. The mass of uniform rope and bucket full of water are m=200g and M=19.9 kg respectively. The increases in potential energy of system is
  359. The work done by a force of i ^ +2 j ^ is zero, when a particle is moving along the line 4 y + k x = 3 . The value of K is
  360. A block is projected upward along a smooth inclined plane of inclination ‘ θ ’. Initial gravitational potential energy of block is zero. The gravitational potential energy of block versus time graph during total time of motion of the block on the inclined plane is
  361. A smaller block of 2kg is placed over a larger block of 5kg. Coefficient of friction between blocks is 0.3 and large block is on smooth surface. A force of 2N is applied on lower block, then work done by friction on upper block in 3 seconds is
  362. The system shown in figure is released from rest. String is massless and pulley is smooth. The loss of potential energy of 4kg block in 3 seconds is
  363. A chain of length l and mass m lies on the surface of a smooth hemisphere of radius R>l with one end tied to the top of the hemisphere. Taking the back of hemisphere as reference line, the gravitational potential energy of the chain is
  364. The velocity of a moving particle varies with distance moved as v = ( 4 + 3 x )   m s − 1 . If mass of the particle is 1kg, then the work done on the particle during the time its displacement changes from x = 1 m to x = 2 m is
  365. A body is thrown on a rough horizontal surface such that the frictional force is varying with distance as f=(8x+5)N . Find the work done by friction on the body if it stops after travelling a distance of 10m
  366. A particle of mass 100g is moving from point A to point B under the action of a force varying with displacement as shown. The work done is
  367. The velocity of a 3kg body varies with time ‘t’ as V= 2+ 1 2 t ms -1 where ‘t’ is in seconds. The work done by the force during the time t=0s to t=2s
  368. Two blocks each of mass ‘m are placed on smooth horizontal surface. They attract each other with a force F= – k r , r is separation between the blocks. The work required to increase the separation between the blocks slowly from a to 4a is k ln   2 x , where x is
  369. The potential energy of a 2kg particle is given by U = ( a x + b y ) J , Where a and b constants, x and y are coordinates of particle in metre. Initially the particle is at rest and at (4a,4b).The coordinates after 2 seconds is ( x a , x b ) , where x is
  370. The potential energy of a positive in a certain field is given by U = a r 2 − b r , where a and b are positive constant and r is the distance from centre of field. The equilibrium position of particle in this field is given by r 0 = n . a b . The value of n is
  371. A force of F = ( 2 x y − 3 z )   j ^ − 8 z k ^ is applied on a particle. The work done by the force in displacing the particle from (0,0,0) to (2,4,0) as shown in figure is
  372. A person of mass 60kg carrying a load of 20kg walks up a stair case. If width and height of each step are 0.25m and 0.2m respectively, the work done by man in walking up 10 steps is (g=10ms − 2 )
  373. Two blocks of mass 3kg and 2kg are connected by a string passing over a light, friction less pulley. If the system is released from rest, net work done by gravity in 2s is (g=10ms − 2 )
  374. A light inextensible string goes over a smooth fixed pulley as shown in the figure connects two blocks of masses 0.36kg and 0.72 kg. Taking g = 10 m s − 2 , find the work done by string on the block of mass 0.36 kg during 1st second after the system is released from rest J
  375. A particle is projected at    60 ∘ to the horizontal with kinetic energy K. The kinetic energy at the position when particle makes 30 ∘ with horizontal is K
  376. A 0.1 kg block is presses against a horizontal spring fixed at one end to compress the spring through 5cm. The spring constant is 100 N m − 1 . The ground is 2m below the spring. The velocity with block hits ground is ( g = 10 m s − 2 ) m s − 1
  377. A car of mass 400kg moving with constant acceleration covers distance between two points 60m apart in 6s. Its speed as it passes second point is 15 m s − 1 . The kinetic energy of car at the first point is kJ
  378. A rod of mass ‘8kg’ hinged at 0 is kept in equilibrium with a spring of force constant 100 N m − 1 as shown in figure. The potential energy stored in the spring is J
  379. The spring and string shown in the figure are ideal and spring constant of spring is 100 N m − 1 . The coefficient of friction between 2m and surface is 0.8 and mass m of hanging block is 1kg. The system is released with spring in unstretched position. The maximum extension of spring in cm is
  380. System shown in figure is released from rest. Pulley and spring are massless and friction is absent everywhere. The speed of 5kg block when 2kg block leaves contact with ground is ( K = 40 N m − 1 ,     g = 10 m s − 2 )
  381. A uniform chain of length ‘L’ is placed on a smooth table of height ‘h’ (h>L) with a length ‘l’ hanging from the edge of table. The chain begins to slide down the table. When the end of the chain is about to leave the edge of table its velocity is K g ( L 2 − l 2 ) 2 L . Where K is
  382. Two ends A and B of a smooth chain of mass ‘m’ and length ‘l’ are situated as shown in figure. If an external agent pulls A till it comes to same level of B, the change in potential energy is m g l x   J . Where x is
  383. A simple pendulum is oscillating without damping. when the displacement of the bob is less than maximum, its acceleration vector a correctly shown in
  384. A small ball is pushed from a height h along a smooth hemispherical bowl. With what speed should the ball be pushed so that it just reaches the top of the opposite end of the bowl? The height of the top of the bowl is R.
  385. Two particles of masses m and 4m have kinetic energies in the ratio of 2:1. What is the ratio of their linear momenta?
  386. A pendulum has a length l. Its bob is pulled aside from its equilibrium position through an angle α and then released. The speed of the bob when it passes through the equilibrium position is given by
  387. 4. Find the velocity of the ball when the string makes an angle of 60 o with vertical. The string length is 2m and mass of the ball is 0.05 kg. Initially at the bottom most point the ball is given a velocity of 10 m/sec
  388. A body of mass m is moving in a circle of radius r with a constant speed v. The force on the body is mv 2 r and is directed towards the centre. What is the work done by this force in moving the body over half the circumference of the circle
  389. If the unit of force and length each be increased by four times, then the unit of energy is increased by
  390. A man pushes a wall and fails to displace it. He does
  391. The same retarding force is applied to stop a train. The train stops after 80 m. If the speed is doubled, then the distance will be
  392. You lift a heavy book from the floor of the room and keep it in the book-shelf having a height 2 m. In this process you take 5 seconds. The work done by you will depend upon
  393. A body of mass m kg is lifted by a man to a height of one metre in 30 sec. Another man lifts the same mass to the same height in 60 sec. The work done by them are in the ratio
  394. A force F = ( 5 i ^ + 3 j ^ ) newton is applied over a particle which displaces it from its origin to the point r = ( 2 i ^ − 1 j ^ ) metres. The work done on the particle is
  395. A body of mass 10 kg is dropped to the ground from a height of 10 metres. The work done (in J) by the gravitational force is ( g = 9 .8   m / sec 2 )
  396. Which of the following is a scalar quantity
  397. The work done in pulling up a block of wood weighing 2 kN for a length of 10m on a smooth plane inclined at an angle of 15° with the horizontal is
  398. A force F = 5 i ^ + 6 j ^ − 4 k ^ N acting on a body, produces a displacement s = 6 i + 5 k m. Work done (in J) by the force is
  399. A force of 5 N acts on a 15 kg body initially at rest. The work done (in J) by the force during the first second of motion of the body is
  400. The work done against gravity in taking 10 kg mass at 1m height in 1sec will be
  401. The energy which an e − acquires when accelerated through a potential difference of 1 volt is called
  402. A body of mass 6kg is under a force which causes displacement in it given by S = t 2 4 metres where t is time. The work done by the force in 2 seconds is
  403. A body of mass 10kg at rest is acted upon simultaneously by two forces 4 N and 3 N at right angles to each other. The kinetic energy of the body at the end of 10 sec is
  404. A force of ( 3 ​  i ^ + 4   j ^ ) Newton acts on a body and displaces it by ( 3   i ^ + 4 ​ j ^ )   m . The work done by the force is
  405. A 50 kg man with 20 kg load on his head climbs up 20 steps of 0.25 m height each. The work done in climbing is
  406. A force F   = 6 i ^ + 2 j ^ − 3 k ^ acts on a particle and produces a displacement of s   = 2 i ^ − 3 j ^ + x k ^ . If the work done is zero, the value of x is
  407. A particle moves from position r 1 =   3 i ^ + 2 j ^ − 6 k ^ to position r 2 = 14 i ^ + 13 j ^ + 9 k ^ under the action of force 4 i ^ + j ^ + 3 k ^   N . The work done will be
  408. A force ( F ) = 3 i ^ + c j ^ + 2 k ^ acting on a particle causes a displacement: ( s )   = − 4 i ^ + 2 j ^ + 3 k ^ in its own direction. If the work done is 6 J, then the value of ‘c’ is
  409. A force F = ( 5 i ^ + 3 j ^ + 2 k ^ ) N is applied over a particle which displaces it from its origin to the point r = ( 2 i ^ − j ^ ) m . The work done on the particle in joules is
  410. The kinetic energy acquired by a body of mass m in travelling some distance s, starting from rest under the actions of a constant force, is directly proportional to
  411. If a force F = 4 i ^ + 5 j ^ causes a displacement s = 3 i ^ + 6 k ^ , work done is
  412. Two bodies of masses 1 kg and 5 kg are dropped gently from the top of a tower. At a point 20 cm from the ground, both the bodies will have the same
  413. A man starts walking from a point on the surface of earth (assumed smooth) and reaches diagonally opposite point. What is the work done by him
  414. Due to a force of ( 6 i ^ + 2 j ^ ) N the displacement of a body is ( 3 i ^ − j ^ ) m , then the work done is ….(in J)
  415. A ball is released from the top of a tower. The ratio of work done by force of gravity in first, second and third second of the motion of the ball is
  416. Two springs of spring constants 1500 N/m and 3000 N/m respectively are stretched with the same force. They will have potential energy in the ratio
  417. The potential energy of a certain spring when stretched through a distance ‘S’ is 10 joule. The amount of work (in joule) that must be done on this spring to stretch it through an additional distance ‘S’ will be
  418. A spring 40 mm long is stretched by the application of a force. If 10 N force required to stretch the spring through 1 mm, then work done (in J) in stretching the spring through 40 mm is
  419. A position dependent force F = 7 − 2 x + 3 x 2   newton acts on a small body of mass 2 kg and displaces it from x = 0 to x = 5   m . The work done in joules is
  420. A body of mass 3 kg is under a force, which causes a displacement in it is given by S = t 3 3 (in m). The work done (in J) by the force in first 2 seconds is
  421. When a 1.0 kg mass hangs attached to a spring of length 50 cm, the spring stretches by 2 cm. The mass is pulled down until the length of the spring becomes 60 cm. What is the amount of elastic energy stored in the spring (in J) in this condition, if g = 10 m/s 2
  422. A spring of force constant 800 N/m has an extension of 5 cm. The work done in extending it from 5 cm to 15 cm is (in J)
  423. A spring when stretched by 2 mm its potential energy becomes 4 J. If it is stretched by 10 mm, its potential energy is equal to
  424. A spring of spring constant 5 × 10 3 N/m is stretched initially by 5 cm from the unstretched position. Then the work required to stretch it further by another 5 cm is (in J)
  425. A mass of 0.5 kg moving with a speed of 1.5 m/s on a horizontal smooth surface, collides with a nearly weightless spring of force constant k = 50 ​  N / m . The maximum compression of the spring would be (in m)
  426. A particle moves in a straight line with retardation proportional to its displacement. Its loss of kinetic energy for any displacement x is proportional to
  427. A spring with spring constant k when stretched through 1 cm, the potential energy is U. If it is stretched by 4 cm. The potential energy will be n times. The value of n is
  428. A spring with spring constant k is extended from x = 0 to x = x 1 . The work done will be
  429. If a long spring is stretched by 0.02 m, its potential energy is U. If the spring is stretched by 0.1 m, then its potential energy will be nU. The value of n is
  430. Which one of the following is not a conservative force
  431. Two bodies of masses m 1 and m 2 have equal kinetic energies. If p 1 and p 2 are their respective momentum, then ratio p 1 : p 2 is equal to
  432. Work done in raising a box depends on
  433. A light and a heavy body have equal momenta. Which one has greater K.E
  434. A body at rest may have
  435. The kinetic energy possessed by a body of mass m moving with a velocity v is equal to 1 2 mv 2 , provided
  436. If the momentum of a body is increased n times, its kinetic energy increases
  437. Two masses of 1 gm and 4 gm are moving with equal kinetic energies. The ratio of the magnitudes of their linear momenta is
  438. A body of mass 2 kg is thrown up vertically with K.E. of 490 joules. If the acceleration due to gravity is 9.8 m/s 2 , then the height at which the K.E. of the body becomes half its original value is given by (in m)
  439. A light and a heavy body have equal kinetic energy. Which one has a greater momentum ?
  440. A free body of mass 8 kg is travelling at 2 meter per second in a straight line. At a certain instant, the body splits into two equal parts due to internal explosion which releases 16 joules of energy(totally taken as KE). Neither part leaves the original line of motion finally
  441. If the K.E. of a particle is doubled, then its momentum will
  442. If the stone is thrown up vertically and return to ground, its potential energy is maximum
  443. A body of mass 2 kg is projected vertically upwards with a velocity of 2   m   sec − 1 . The K.E. of the body just before striking the ground is (in J)
  444. Two bodies of different masses m 1 and m 2 have equal momenta. Their kinetic energies E 1 and E 2 are in the ratio
  445. If the kinetic energy of a body increases by 0.1%, the percent increase of its momentum will be (in %)
  446. If velocity of a body is twice of previous velocity, then kinetic energy will become ….times
  447. A sphere of mass m, moving with velocity V, enters a hanging bag of sand and stops. If the mass of the bag is M and it is raised by height h, then the velocity of the sphere was
  448. Two bodies of masses m and 2m have same momentum. Their respective kinetic energies E 1 and E 2 are in the ratio
  449. Kinetic energy of a particle is decreased by 3% without change in its mass. Find the percentage of change in its momentum.
  450. Kinetic energy of a particle is increased by 50 % without change in its mass. Find the percentage change in its momentum.
  451. If a lighter body (mass M 1 and velocity V 1 ) and a heavier body (mass M 2 and velocity V 2 ) have the same kinetic energy, then
  452. The force constant of a weightless spring is 16 N/m. A body of mass 1.0 kg suspended from it is pulled down through 5 cm and then released. The maximum kinetic energy of the system (spring + body) will be
  453. Two bodies with kinetic energies in the ratio of 4 : 1 are moving with equal linear momentum. The ratio of their masses is
  454. A bullet is fired from a rifle. If the rifle recoils freely, then the kinetic energy of the rifle is
  455. If the water falls from a dam into a turbine wheel 19.6 m below, then the velocity of water (in m/s) at the turbine is ( g = 9 .8   m / s 2 )
  456. Two bodies of masses 2m and m have their K.E. in the ratio 8 : 1, then their ratio of momenta is
  457. A bomb of 12 kg divides in two parts whose ratio of masses is 1 : 3. If kinetic energy of smaller part is 216 J, then momentum of bigger part in kg-m/sec will be
  458. A 4 kg mass and a 1 kg mass are moving with equal kinetic energies. The ratio of the magnitudes of their linear momenta is
  459. If the increase in the kinetic energy of a body is 22%, then the increase in the momentum will be (in %)
  460. If a body of mass 200 g falls from a height 200 m and its total P.E. is converted into K.E. at the point of contact of the body with earth surface, then what is the decrease in P.E. (in J) of the body at the contact ( g = 10   m / s 2 )
  461. If momentum is increased by 20%, then K.E. increases by %
  462. The kinetic energy of a body of mass 2 kg and momentum of 2 Ns is …J
  463. The decrease in the potential energy of a ball of mass 20 kg which falls from a height of 50 cm is
  464. An object of 1 kg mass has a momentum of 10 kg m/sec then the kinetic energy of the object will be (in J)
  465. A ball is released from certain height. It loses 50% of its kinetic energy on striking the ground. It will attain a height again equal to
  466. A 0.5 kg ball is thrown up with an initial speed 14 m/s and reaches a maximum height of 8.0m. How much energy is dissipated by air drag acting on the ball during the ascent (in J) (take g=9.8 m/s 2 )
  467. An ice cream has a marked value of 700 kcal. How many kilowatt- hour of energy will it deliver to the body as it is digested
  468. What is the velocity of the bob of a simple pendulum at its mean position, if it is able to rise to vertical height of 10 cm (Take g = 9 .8   m / s 2 )
  469. A particle of mass ‘m’ and charge ‘q’ is accelerated through a potential difference of ‘V’ volt. Its energy is
  470. A running man has half the kinetic energy of that of a boy of half of his mass. The man speeds up by 1m/s so as to have same K.E. as that of the boy. The original speed of the man will be
  471. The mass of two substances are 4gm and 9gm respectively. If their kinetic energies are same, then the ratio of their momenta will be
  472. A machine which is 75 percent efficient, uses 12 joules of energy in lifting up a 1 kg mass through a certain distance. The mass is then allowed to fall through that distance. The velocity at the end of its fall is (in ms − 1 )
  473. Two bodies moving towards each other collide and move away in opposite directions. There is some rise in temperature of bodies because a part of the kinetic energy is converted into
  474. Two bodies of masses m and 4 m are moving with equal K.E. The ratio of their linear momentums is
  475. A stationary particle explodes into two particles of a masses m 1 and m 2 which move in opposite directions with velocities v 1 and v 2 The ratio of their kinetic energies E 1 /E 2 is
  476. A bullet moving with a speed of 100 ms -1 can just penetrate two planks of equal thickness. Then the number of such planks penetrated by the same bullet when the speed is doubled will be
  477. A particle of mass m 1 is moving with a velocity v 1 and another particle of mass m 2 is moving with a velocity v 2 . Both of them have the same momentum but their different kinetic energies are E 1 and E 2 respectively. If m 1 > m 2 then
  478. A ball of mass 2kg and another of mass 4kg are dropped together from a 60 feet tall building. After a fall of 30 feet each towards earth, their respective kinetic energies will be in the ratio of
  479. Relation between kinetic energy K and momentum p of a particle is p = 2 K m Find the percentage of change in p if K is decrease by 36%
  480. Relation between kinetic energy K and momentum p of a particle is p = 2 K m Find the percentage of change in p if K is increased by 1%
  481. Four particles given, have same momentum which has maximum kinetic energy
  482. A body moving with velocity v has momentum and kinetic energy numerically equal. What is the value of v
  483. If a man increase his speed by 2 m/s, his K.E. is doubled, the original speed of the man is
  484. Which among the following, is a form of energy
  485. A particle of mass m moving with velocity V 0 strikes a simple pendulum of mass m and sticks to it. The maximum height attained by the pendulum will be
  486. A body of mass 5 kg is moving with a momentum of 10 kg-m/s. A force of 0.2 N acts on it in the direction of motion of the body for 10 seconds. The increase in its kinetic energy is (in J)
  487. Masses of two substances are 1 g and 9 g respectively. If their kinetic energies are same, then the ratio of their momentum will be
  488. If the momentum of a body increases by 0.01%, its kinetic energy will increase by (%)
  489. A block of mass m initially at rest is dropped from a height h on to a spring of force constant k. The maximum compression in the spring is x then
  490. A spherical ball of mass 20 kg is stationary at the top of a hill of height 100 m. It slides down a smooth surface to the ground, then climbs up another hill of height 30 m and finally slides down to a horizontal base at a height of 20 m above the ground. The velocity attained by the ball is
  491. The block of mass M moving on the frictionless horizontal surface collides with the spring of spring constant K and compresses it by length L. The maximum momentum of the block after collision is
  492. A mass of 100g strikes the wall with speed 5m/s at an angle as shown in figure and it rebounds with the same speed. If the contact time is 2 × 10 − 3   sec , what is the force applied on the mass by the wall
  493. If a force F is applied on a body and it moves with a velocity v, the power will be
  494. A body of mass m accelerates uniformly from rest to v 1 in time t 1 . As a function of time t, the instantaneous power delivered to the body is
  495. A man is riding on a cycle with velocity 7.2 km/hr up a hill having a slope 1 in 20. The total mass of the man and cycle is 100 kg. The power of the man is (in W)
  496. An engine develops 10 kW of power. How much time will it take to lift a mass of 200 kg to a height of 40 m. ( g = 10   m / sec 2 )
  497. A car of mass ‘m’ is driven with acceleration ‘a’ along a straight level road against a constant external resistive force ‘R’. When the velocity of the car is ‘V’, the rate at which the engine of the car is doing work will be
  498. The average power required to lift a 100 kg mass through a height of 50 metres in approximately 50 seconds would be (J/s) Take g =9.8m/s 2
  499. A 10 HP motor pumps out water from a well of depth 20m and fills a water tank of volume 22380 litre at a height of 10m from the ground. The running time of the motor to fill the empty water tank is ( g = 10 ms − 2 )
  500. A force applied by an engine of a train of mass 2 .05 × 10 6 kg changes its velocity from 5 m/s to 25 m/s in 5 minutes. The power of the engine is
  501. A 60 kg man runs up a staircase in 12 seconds while a 50 kg man runs up the same staircase in 11, seconds, the ratio of the rate of doing their work is
  502. A pump motor is used to deliver water at a certain rate from a given pipe. To obtain twice as much water from the same pipe in the same time, power of the motor has to be increased to
  503. What average horsepower is developed by an 80 kg man while climbing in 10 s a flight of stairs that rises 6 m vertically
  504. A car of mass 1000 kg accelerates uniformly from rest to a velocity of 54 km/hour in 5 s. The average power (W) of the engine during this period in watts is (neglect friction)
  505. A quarter horse power motor runs at a speed of 600 r.p.m. Assuming 40% efficiency the work done by the motor in one rotation will be
  506. An engine pumps up 100 kg of water through a height of 10 m in 5 s. Given that the efficiency of the engine is 60% . If g = 10 ms − 2 , the power of the engine is
  507. The power of pump, which can pump 200 kg of water to a height of 50 m in 10 sec, will be
  508. The coefficient of restitution e for a perfectly elastic collision is
  509. Two perfectly elastic particles P and Q of equal mass travelling along the line joining them with velocities 15 m/sec and 10 m/sec. After collision, their velocities respectively (in m/sec) will be
  510. A lead ball strikes a wall and falls down, a tennis ball having the same mass and velocity strikes the wall and bounces back. Check the correct statement
  511. A heavy steel ball of mass greater than 1 kg moving with a speed of 2 m sec -1 collides head on with a stationary ping-pong ball of mass less than 0.1 gm. The collision is elastic. After the collision the ping-pong ball moves approximately with speed
  512. In an elastic collision of two particles the following is conserved
  513. A smooth sphere of mass M moving with velocity u directly collides elastically with another sphere of mass m at rest. After collision their final velocities are V and v respectively. The value of v is
  514. A body of mass m having an initial velocity v, makes head on collision with a stationary body of mass M. After the collision, the body of mass m comes to rest and only the body having mass M moves. This will happen only when
  515. A particle of mass m moving with horizontal speed 6 m/sec as shown in figure. If m < < M then for one dimensional elastic collision, the speed of lighter particle after collision will be
  516. A particle of mass m moving with a velocity V makes a head on elastic collision with another particle of same mass initially at rest. The velocity of the first particle after the collision will be
  517. Two equal masses m 1 and m 2 moving along the same straight line with velocities + 3 m/s and – 5 m/s respectively collide elastically. Their velocities after the collision will be respectively
  518. A rubber ball is dropped from a height of 5 m on a planet where the acceleration due to gravity is not known. On bouncing, it rises to 1.8 m. The ball loses its velocity on bouncing by a factor of
  519. A metal ball falls from a height of 32 metre on a steel plate. If the coefficient of restitution is 0.5, to what height will the ball rise after second bounce
  520. A ball of mass 10 kg is moving with a velocity of 10 m/s. It strikes another ball of mass 5 kg which is moving in the same direction with a velocity of 4 m/s. If the collision is elastic, their velocities after the collision will be, respectively
  521. A body of mass 2 kg collides with a wall with speed 100 m/s and rebounds with same speed. If the time of contact was 1/50 second, the force exerted on the wall is
  522. A ball of weight 0.1 kg coming with speed 30 m/s strikes with a bat and returns in opposite direction with speed 40 m/s, then the impulse is (Taking final velocity as positive)
  523. A billiard ball moving with a speed of 5 m/s collides with an identical ball originally at rest. If the first ball stops after collision, then the second ball will move forward with a speed of
  524. If two balls each of mass 0.06 kg moving in opposite directions with speed 4 m/s collide and rebound with the same speed, then the impulse imparted to each ball due to other is
  525. A ball of mass m falls vertically to the ground from a height h 1 and rebound to a height h 2 . The change in momentum of the ball on striking the ground is
  526. A body of mass m 1 moving with a velocity 3 ms –1 collides with another body at rest of mass m 2 . After collision the velocities of the two bodies are 2 ms –1 and 5ms –1 respectively along the direction of motion of m 1 . The ratio m 1 / m 2 is
  527. 100 g of a iron ball having velocity 10 m/s collides with a wall at an angle 30 o and rebounds with the same angle. If the period of contact between the ball and wall is 0.1 second, then the force experienced by the ball is
  528. Two bodies having same mass 40 kg are moving in opposite directions, one with a velocity of 10 m/s and the other with 7 m/s If they collide and move as one body, the velocity of the combination is (m/s)
  529. A particle falls from a height h upon a fixed horizontal plane and rebounds. If e is the coefficient of restitution, the total distance travelled before rebounding has stopped is
  530. The bob A of a simple pendulum is released when the string makes an angle of 45 o with the vertical. It hits another bob B of the same material and same mass kept at rest on the table. If the collision is elastic
  531. A big ball of mass M, moving with velocity u strikes a small ball of mass m, which is at rest. Finally small ball obtains velocity u and big ball v. Then what is the value of v
  532. A body of mass 5 kg moving with a velocity 10 m/s collides with another body of the mass 20 kg at rest and comes to rest. The velocity of the second body due to collision is
  533. A ball of mass m moving with velocity V, makes a head on elastic collision with a ball of the same mass moving with velocity 2V towards it. Taking direction of V as positive velocities of the two balls after collision are
  534. A body of mass M 1 collides elastically with another mass M 2 at rest. There is maximum transfer of energy when
  535. A body of mass 2 kg makes an elastic collision with another body at rest and continues to move in the original direction with one fourth of its original speed. The mass of the second body which collides with the first body is
  536. In the elastic collision of objects
  537. A body of mass M moves with velocity v and collides elastically with a another body of mass m (M>>m) at rest then the velocity of body of mass m is
  538. Two particles having position vectors r 1 = ( 3 i ^ + 5 j ^ ) meters and r 2 = ( − 5 i ^ − 3 j ^ ) meters are moving with velocities v 1 = ( 4 i ^ + 3 j ^ )   m / s and v 2 = ( α   i ^ + 7 j ^ ) m / s . If they collide after 2 seconds, the value of ‘ α ‘ is
  539. A neutron makes a head-on elastic collision with a stationary deuteron. The fractional energy loss of the neutron in the collision is
  540. Two masses m A and m B moving with velocities v A and v B in opposite directions collide elastically. After that the masses m A and m B move with velocity v B and v A respectively. The ratio ( m A / m B ) is
  541. A ball is allowed to fall from a height of 10 m. If there is 40% loss of energy due to impact, then after one impact ball will go up to (in m)
  542. Which of the following statements is true
  543. The quantities remaining constant in a collision are
  544. A ball is projected vertically down with an initial velocity from a height of 20 m onto a horizontal floor. During the impact it loses 50% of its energy and rebounds to the same height. The initial velocity of its projection is (in m/s) [Take g = 10 m/s 2 ]
  545. A sphere collides with another sphere of identical mass. After collision, the two spheres move. The collision is inelastic. Then the angle between the directions of the two spheres is
  546. A particle of mass m moving eastward with a speed v collides with another particle of the same mass moving northward with the same speed v. The two particles coalesce on collision. The new particle of mass 2m will move in the north-easterly direction with a velocity
  547. The coefficient of restitution e for a perfectly inelastic collision is
  548. When two bodies stick together after collision, the collision is said to be
  549. A bullet of mass a and velocity b is fired into a large block of mass c. The final velocity of the system is
  550. A mass of 10 gm moving with a velocity of 100 cm/s strikes a pendulum bob of mass 10 gm. The two masses stick together. The maximum height (in cm) reached by the system now is ( g = 10   m / s 2 )
  551. A completely inelastic collision is one in which the two colliding particles
  552. A bullet hits and gets embedded in a solid block resting on a horizontal frictionless table. What is conserved ?
  553. A 50 g bullet moving with velocity 10 m/s strikes a block of mass 950 g at rest and gets embedded in it. The loss in kinetic energy will be (in %)
  554. A particle of mass m moving with velocity v strikes a stationary particle of mass 2m and sticks to it. The speed of the system will be
  555. If a skater of weight 3 kg has initial speed 32 m/s and second one of weight 4 kg has 5 m/s. After collision, they have speed (couple) 5 m/s. Then the loss in K.E. is
  556. A ball is dropped from height 10 m. Ball is embedded in sand 1 m and stops, then
  557. A metal ball of mass 2 kg moving with a velocity of 36 km/h has an head on collision with a stationary ball of mass 3 kg. If after the collision, the two balls move together, the loss in kinetic energy due to collision is
  558. Which of the following is not a perfectly inelastic collision
  559. A mass of 20 kg moving with a speed of 10m/s collides with another stationary mass of 5 kg. As a result of the collision, the two masses stick together. The kinetic energy of the composite mass will be
  560. The quantity that is not conserved in an inelastic collision is
  561. A neutron having mass of 1 .67 × 10 − 27 kg and moving at 10 8 m / s collides with a deutron at rest and sticks to it. If the mass of the deutron is 3 .34 × 10 − 27 kg then the speed of the combination is
  562. A body of mass 40kg having velocity 4 m/s collides with another body of mass 60kg having velocity 2 m/s. If the collision is inelastic, then loss in kinetic energy (in J) will be
  563. A body of mass m 1 is moving with a velocity V. It collides with another stationary body of mass m 2 . They get embedded. At the point of collision, the velocity of the system
  564. A bullet of mass m moving with velocity v strikes a block of mass M at rest and gets embedded into it. The kinetic energy of the composite block will be
  565. In an inelastic collision, what is conserved
  566. Two bodies of masses 0.1 kg and 0.4 kg move towards each other with the velocities 1 m/s and 0.1 m/s respectively, After collision they stick together. In 10 sec the combined mass travels
  567. Which of the following is not an example of perfectly inelastic collision
  568. A body of mass 4 kg moving with velocity 12 m/s collides with another body of mass 6 kg at rest. If two bodies stick together after collision, then the loss of kinetic energy of system is
  569. A ball hits the floor and rebounds after inelastic collision. In this case
  570. If W 1 , W 2 and W 3 represent the work done in moving a particle from A to B along three different paths 1, 2 and 3 respectively (as shown) in the gravitational field of a point mass m, find the correct relation between W 1 , W 2 and W 3
  571. A uniform chain of length L and mass M is lying on a smooth table and one third of its length is hanging vertically down over the edge of the table. If g is acceleration due to gravity, the work required to pull the hanging part on to the table is
  572. A particle free to move along the x-axis has potential energy given by U ( x ) = k [ 1 − exp ( − x 2 ) ] for − ∞ ≤ x ≤ + ∞ , where k is a positive constant of appropriate dimensions. Then
  573. An open knife edge of mass ‘m’ is dropped from a height ‘h’ on a wooden floor. If the blade penetrates upto the depth ‘d’ into the wood, the average resistance offered by the wood to the knife edge is
  574. Consider the following two statements 1. Linear momentum of a system of particles is zero 2. Kinetic energy of a system of particles is zero Then
  575. A body is moved along a straight line by a machine delivering constant power. The distance moved by the body in time t is proportional to
  576. Consider elastic collision of a particle of mass m moving with a velocity u with another particle of the same mass at rest. After the collision the projectile and the struck particle move in directions making angles θ 1 and θ 2 respectively with the initial direction of motion. The sum of the angles. θ 1 + θ 2 , is
  577. A body of mass m moving with velocity v collides head on with another body of mass 2m which is initially at rest. The ratio of K.E. of colliding body before and after collision will be
  578. The relationship between force and position is shown in the figure given (in one dimensional case). The work done by the force in displacing a body from x = 1 cm to x = 5 cm is
  579. The pointer reading v/s load graph for a spring balance is as given in the figure. The spring constant is
  580. A 10kg mass moves along x-axis. Its acceleration as a function of its position is shown in the figure. What is the total work done on the mass by the force as the mass moves from x = 0 to x = 8   cm
  581. The graph between the resistive force F acting on a body and the distance covered by the body is shown in the figure. The mass of the body is 25 kg and initial velocity is 2 m/s. When the distance covered by the body is 4 m, its kinetic energy would be (in J)
  582. A particle is dropped from a height h. A constant horizontal velocity is given to the particle. Taking g to be constant every where, kinetic energy E of the particle w. r. t. time t is correctly shown in
  583. A particle of mass 0.1 kg is subjected to a force which varies with distance as shown in fig. If it starts its journey from rest at x = 0 , its velocity at x = 12   m is
  584. The potential energy of a system is represented in the first figure. the force acting on the system will be represented by
  585. A particle, initially at rest on a frictionless horizontal surface, is acted upon by a horizontal force which is constant in size and direction. A graph is plotted between the work done (W) on the particle, against the speed of the particle, (v). If there are no other horizontal forces acting on the particle the graph would look like
  586. The potential energy of a particle varies with distance x as shown in the graph. The force acting on the particle is zero at
  587. The graph between E and v is
  588. The relationship between the force F and position x of a body is as shown in figure. The work done in displacing the body from x = 1 m to x = 5 m will be
  589. How much work does a pulling force of 40 N do on the 20 kg box in pulling it 8 m across the floor at a constant speed. The pulling force is directed at 60° above the horizontal
  590. A horizontal force of 5 N is required to maintain a velocity of 2 m/s for a block of 10 kg mass sliding over a rough surface. The work done by this force in one minute is
  591. Work done in time t on a body of mass m which is accelerated from rest to a speed v in time t 1 as a function of time t is given by
  592. What is the shape of the graph between the speed and kinetic energy of a body
  593. The slope of kinetic energy displacement curve of a particle in motion is
  594. The energy required to accelerate a car from 10 m/s to 20 m/s is how many times the energy required to accelerate the car from rest to 10 m/s
  595. A body of mass 2 kg slides down a curved track which is quadrant of a circle of radius 1 metre. All the surfaces are frictionless. If the body starts from rest, its speed at the bottom of the track is
  596. The kinetic energy of a body decreases by 36%. The decrease in its momentum is
  597. A bomb of mass 3m kg explodes into two pieces of mass m kg and 2m kg. If the velocity of m kg mass is 16 m/s, the total kinetic energy released in the explosion is
  598. A neutron travelling with a velocity v and K.E. E collides perfectly elastically head on with the nucleus of an atom of mass number A at rest. The fraction of total energy retained by neutron is
  599. A body of mass m 1 moving with uniform velocity of 40 m/s collides with another mass m 2 at rest and then the two together begin to move with uniform velocity of 30 m/s. The ratio of their masses m 1 m 2 is
  600. Six identical balls are lined in a straight groove made on a horizontal frictionless surface as shown. Two similar balls each moving with a velocity v collide elastically with the row of 6 balls from left. What will happen
  601. A man places a chain of mass m and length l on a table slowly. Initially, the lower end of the chain just touches the table. The man brings down the chain by length l/2. Work done by the man in this process is
  602. A block attached to a spring, pulled by a constant horizontal force, is kept on a smooth surface as shown in figure. Initially, the spring is in the natural length state. Then the maximum positive work that the applied force F can do is (given that spring does not break)
  603. The given plot shows the variation of U, the potential energy of interaction between two particles, with the distance separating them r. 1. B and D are equilibrium points. 2. C is a point of stable equilibrium. 3. The force of interaction between the two particles is attractive between points C and B, and repulsive between points D and E on the curve. 4. The force of interaction between the particles is repulsive between points C and A. Which of the above statements are correct?
  604. A particle is projected with a velocity , making an angle θ with the horizontal. The instantaneous power of the gravitational force
  605. A particle is projected vertically upwards with a speed of 16 ms -1 . After some time, when it again passes through the point of projection, its speed is found to be 8 ms -1 . It is known that the work done by air resistance is same during upward and downward motion. Then the maximum height attained by the particle is (take g = 10 ms -2 )
  606. A machine delivers power to a body which is proportional to velocity of the body. If the body starts with a velocity which is almost negligible, then the distance covered by the body is proportional to
  607. Two constant forces F 1 and F 2 act on a body of mass 8 kg. These forces displace the body from point P (1, -2, 3) to Q (2, 3, 7) in 2s starting from rest. Force F 1 is of magnitude 9 N and is acting along vector ( 2 i ^ − 2 j ^ + k ^ ) . Work done by the force F 2 is
  608. A particle of mass m slides along a curved-flat-curved track. The curved portions of the track are smooth. If the particle is released at the top of one of the curved portions, the particle comes to rest at flat portion of length I and of μ = μ kinetic after covering a distance of
  609. In the position shown in figure, the spring is at its natural length. The block of mass m is given a velocity v 0 towards the vertical support at t = 0. The coefficient of friction between the block and the surface is given by μ = αx , where α is a positive constant and x is the position of the block from its starting position. The block comes to rest for the first time at x, which is
  610. A block of mass m is lying at rest at point P of a wedge having a smooth semi-circular track of radius R. What should be the minimum value of a 0 so that the mass can just reach point Q?
  611. A stationary body of mass 3 kg explodes into three equal pieces. Two of the pieces fly off at right angles to each other. One with a velocity of 2 i ^ m/s and the other with a velocity of 3 j ^ m/s. If the explosion takes place in 10 -5 s, the average force acting on the third piece in newtons is
  612. A particle of mass 4m is projected from the ground at some angle with horizontal. Its horizontal range is R. At the highest point of its path it breaks into two pieces of masses m and 3m, respectively, such that the smaller mass comes to rest. The larger mass finally falls at a distance x from the point of projection, where x is equal to
  613. A gun which fires small balls of mass 20 g is firing 20 balls per second on the smooth horizontal table surface ABCD. If the collision is perfectly elastic and balls are striking at the centre of table with a speed of 5 m/s at an angle of 60° with the vertical just before collision, then force exerted by one of the legs on ground is (assume total weight of the table is 0.2 kg)
  614. Two identical billiard balls undergo an oblique elastic collision. Initially, one of the balls is stationary. If the initially stationary ball after collision moves in a direction which makes an angle of 37 o with direction of initial motion of the moving ball, then the angle through which initially moving ball will be deflected is
  615. An object of mass 2 kg is kept in a lift which moves upwards. Velocity of the lift varies with time as shown in the graph. Work done (in J) by normal contact force of the lift on the block, during the time t = 0 to t = 4 s is .
  616. A square carpet of a mass of 20 kg is dragged from one room into another as shown in the figure. The width of the corridor and the carpet is the same, i.e., 2 m. The friction coefficient is 0.1 at the end of the first room and 0.2 at the other end, in the corridor it changes linearly from 0.1 to 0.2. The carpet presses the floor uniformly. Find the amount of work (in J) that must be done to drag the carpet slowly from the first room to the other.
  617. The spring block system lies on a smooth horizontal surface. The free end of the spring is being pulled towards right with constant speed v 0 = 2 m/s. At t = 0 sec, the spring of constant k = 100 N/cm is unstretched and the block has a speed 1 m/s to the left. The maximum extension of the spring (in cm) is .
  618. An insect jumps from ball A onto ball B, which are suspended from inextensible light strings each of length L = 8 cm. The mass of each ball and insect is same. What should be the minimum relative velocity (in ms -1 ) of jump of insect w.r.t. ball A, if both the balls manage to complete the full circle?
  619. A block of mass m is released from rest at point A. The compression in spring (force constant k) when the speed of block is maximum is found to be nmgcos ⁡ θ 4 k . What should be the value of n?
  620. A force F acting on an object varies with distance x as shown in the figure. The work done by the force in moving the object from x = 0 to x = 8 m is
  621. A crane lifts a mass of 100 kg to a height of 10 m in 20 s. The power of the crane is ( Take g = 10 ms − 2 )
  622. A spherical ball A of mass 4 kg, moving along a straight line strikes another spherical ball B of mass 1 kg at rest. After the collision, A and B move with velocities v 1 ms -1 and v 2 ms -1 respectively making angles of 30° and 60° with respect to the original direction of motion of A. The ratio v 1 v 2 will be
  623. A bolt of mass 0.2 kg falls from the ceiling of an elevator moving down with an uniform speed of 5 ms -1 . It hits the floor of the elevator (length of the elevator = 5 m) and does not rebound. The amount of heat produced by the impact is (Take g = 10 ms -2 )
  624. A block of mass 1 kg is pushed up a surface inclined to horizontal at an angle of 30° by a force of 10 N parallel to the inclined surface as shown in the figure. The coefficient of friction between block and the incline is 0.1. If the block is pushed up by 10 m along the incline, then the work against gravity is (Take g = 10 m s -2 )
  625. A 1 kg block situated on a rough incline is connected to a spring of negligible mass having spring constant 100 Nm − 1 as shown in the figure. The block is released from rest with the spring in the unstretched position. The block moves 10 cm down the incline before coming to rest. The coefficient of friction between the block and the incline is (Take g = 10 ms − 2 and assume that the pulley is frictionless)
  626. In the figure shown, the heavy ball of mass 2m rests on the horizontal surface and the lighter ball of mass m is dropped from a height h > 2l. At the instant the string gets taut, the upward the velocity of the heavy ball will be
  627. In the position shown in figure, the spring is at its natural length. The block of mass m is given a velocity v 0 towards the vertical support at t = 0. The coefficient of friction between the block and the surface is given by μ = αx , where α a positive constant and x is the position of the block from its starting position. The block comes to rest for the first time at x, which is
  628. In the figure shown, the cart of mass 6m is initially at rest. A particle of mass m is attached to the end of the light rod which can rotate freely about A. If the rod is released from rest in a horizontal position shown, determine the velocity v rel of the particle with respect to the cart when the rod is vertical.
  629. The potential energy of a particle is determined by the expression U = α x 2 + y 2 , where α is a positive constant. The particle begins to move from a point with coordinates (3, 3), only under the action of potential field force. Then its kinetic energy T at the instant when the particle is at a point with the coordinates (1, 1) is
  630. Power supplied to a particle of mass 2 kg varies with time as P = 3 t 2 2 watt, here t is in second. If the velocity of particle at t = 0 is v = 0, the velocity of particle at time t = 2 s will be
  631. A ball of mass m moving at a speed v makes a head-on collision with an identical ball at rest. The kinetic energy of the balls after the collision is 3/4 th of the original. If the coefficient of restitution is e, find the value of e 2 .
  632. Sand drops vertically at the rate of 2 kgs –1 on to a conveyor belt moving horizontally with a velocity of 0.1 ms –1 . The extra power needed to keep the belt moving is
  633. A particle is taken from point A to point B via the path ACB and then come back to point A via the path BDA. What is the work done by gravity on the body over this closed path, if the motion of the particle is in the vertical plane?
  634. A 5.0 kg box rests on a horizontal surface. The coefficient of kinetic friction between the box and the surface is 0.5. A horizontal force pulls the box at constant velocity for 10 cm. The work done by the applied horizontal force and the frictional force are respectively (take g=10m/s 2 )

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