A small block slides with velocity v 0 = 0 . 5 gr on the horizontal frictionless surface as shown in the fig. The block leaves the surface at point C. The angle θ in the figure is:

A vehicle is moving with uniform speed along horizontal, concave and convex surface roads. The surface on which, the normal reaction on the vehicle is maximum is

The length of a simple pendulum is 50 cm and mass of its bob is 0.1 kg. The bob is given a velocity 5 m/s along horizontal direction when the bob is at lowest position and the bob describes vertical circle of radius equal to length of pendulum. The position in the vertical circle, where the tension in the string is 4.5 N is (g = 10ms –2 )

A vehicle is moving with a velocity v on a curved road of width b and radius of curvature R . For counteracting the centrifugal force on the vehicle the difference in elevation required in between the outer and inner edges of the road is

A car of mass 1000 kg negotiates a banked curve of radius 90 m on a frictionless road. If the banking angle is 45 0 , the speed of the car is [CBSE AIPMT 2012]

A particle moves in a circular path with decreasing speed. Which of the folowing is correct.

A cyclist on a level road takes a sharp circular turn of radius 3m ( g = 10 m s – 2 ). If the coefficient of static friction between the cycle tyres and the road is 0.2, at which of the following speeds will the cyclist not skid while taking the turn ?

A small sphere is suspended by a string of length 3 m. If the sphere rotates in a horizontal circle of radius 2m with uniform speed, the time period of rotation of the sphere is

Skidding occurs when the maximum frictional force of a flat road on a car is

A car is travelling at 36 kmph on a road. If µ = 0.5 between the tyres and the road, the minimum turning radius of the car is (g=10ms –2 )

For a car taking a turn on a horizontal surface, let N 1 and N 2 be the normal reactions of the road on the inner and outer wheels respectively.

In a conical pendulum, the bob is rotated with different angular velocities and tension in the string is calculated for different values of ω . Which of them is correct graph between T & ω .

A bob of mass m is suspended by a light string of length L. It is imparted a horizontal velocity v 0 at the lowest point A such that it completes a semi-circular trajectory in the vertical plane with the B string becoming slack only on reaching Q the topmost point, C. Column-I Column-II (i) Velocity v 0 is (p) 3 (ii) Velocity at point B is (q) gL (iii) Velocity at point C is r) 5 gL (iv) Ratio of kinetic energy at B and C is (s) 3 gL Now match the Column-I with Column-II and mark the correct choice from the codes given below. Codes

A ball of mass 0.5kg is attached to the end of a string having length 0.5m. The ball is rotated on a horizontal circular path about vertical axis. The maximum tension that the string can bear is 324N. The maximum possible value of angular velocity of ball in (rad/s)

An object is moving in a circle of radius 100 m with a constant speed of 31.4 m s – 1 . What is its average speed for one complete revolution?

A motorcyclist riding at 36 kmh -1 has to turn a corner. Find the least radius of the curve, he should follow for safe travelling, if the coefficient of friction between the tyres and the road is 0.2.

Two points of a rod move with velocities 3v and v perpendicular to the rod and in the same direction, separated by a distance r. then the angular velocity of the rod is

A circular disc is rotating with a varying speed u =(2t-4) m/s, where t is in second. An object is placed in the disc. The pseudo fore on the object is

A mass m moves in a circle on a smooth horizontal plane with velocity ν 0 at a radius R 0 . The mass is attached to a string which passes through a smooth hole in the plane as shown. The tension in the string is increased gradually and finally m moves in a circle of radius R 0 2 . The final value of the kinetic energy is

If the angular momentum of a body of mass ‘m’ rotating in a circle of radius ‘r’ is ‘L’ then the centripetal force on it is

A small sphere of mass m is suspended from a fringe by a light rigid rod of length l . The rod can swing in a vertical circle with what minimum velocity should the sphere be projected horizontally for which it will complete a vertical revolution ?

Statement -A : The net acceleration of a particle in circular motion is always along the radius of the circle towards the centre Statement -B : The velocity vector of a particle at a point is always along the tangent to the path of the particle at that point

Identify the increasing order of angular velocities of following a) Earth rotating about its own axis b) Hour’s hand of clock c) Seconds hand of clock d) Fly wheel of radius 2m making 300 r.p.m.

A particle of mass m is tied to a light string and rotated with a speed v along a circular path of radius r. If T is tension in the string and mg is gravitational force on the particle then, the actual forces acting on the particle are

A vehicle moves safe on a rough, curved and unbanked road. Then a) The direction of static friction is radially out wards b) The direction of static friction is radially inwards c) The direction of kinetic friction is tangential to curved path d) Static friction does not exist

Two point size bodies of same mass are knotted to a horizontal string one at the end, and the other at the mid point of it. The string is rotated in horizontal plane with the other end as centre. If T is tension in the string between centre of circle and first body then the tension in the string between the two bodies is

A 5 kg body is rotated in a vertical circle with a constant speed of 4 ms –1 using a string of length 1 m, when the tension in the string is 31N, then the body will be

The tube AC from a quarter circle in a vertical plane. The ball B has an area of crosssection slightly smaller than that of the tube, and can moves without friction through it. B is placed at A and displaced slightly. It will

In gravity- free space, a particle is in contact with the inner surface of a hollow vertical cylinder and moves in horizontal circular path along the surface. There is some friction between the particle and the surface. The retardation of the particle is

A stone of mass 1kg is tied to one end of a string of length 0.5 m. It is whirled in a vertical circle. If the maximum tension in the string is 58.8N, the velocity at the top is

A pendulum with a bob of mass m is suspended from a horizontal platform. The platform is given a horizontal uniform acceleration. The breaking tension in the light string of the pendulum is( 2/√3 ) mg. Find the work done by the extreme tension T on the bob in the first one sec.

A small block of mass m is attached to one end of a string OA of length l as shown in figure. The end O of the string is fixed at point O and the block is released with the string horizontal. If m = 2 k g , find the maximum tension induced in the string. Take g = 10 m / s 2 .

A particle of mass 100 gm tied to a light string of length 40 cm and related along a vertical circular path. What should be the minimum speed at the highest point of its path so that the string does not become slack at any position?

A train A runs from east to west and another train B of the same mass runs from west to east at the same speed along the equator. A presses the track with a force F 1 and B presses the track with a force F 2 .

A circular road of radius R is banked for a speed v = 40 km/hr. A car of mass m attempts to go on the circular road, the friction coefficient between the tyre and road is negligible:

A mass m is attached to a thin wire and whirled in a vertical circle. The wire is most likely to break when

A particle of mass m is suspended from the ceiling through a string of length L. The particle moves in a horizontal circle of radius r . The speed of the particle is

A small coin is placed on a flat horizontal turn table. The turn table is observed to make three revolutions in 3.14 sec. What is the coefficient of static friction between the coin and turn table if the coin is observed to slide off the turn table when it is greater than 10cm from the centre of turn table

A car is moving on a circular level road of radius of curvature 300m. If the coefficient of friction is 0.3 and acceleration due to gravity is 10m/s 2 . The maximum speed the car can have is

A wheel rotates at 50 rpm about its axis. The angular retardation that can stop the wheel in one minute ·is

A car wheel is rotated to uniform angular acceleration about its axis. Initially, its angular velocity is zero. It rotates through an angle θ 1 in the first 2 s. In the next 2 s, it rotates through an additional angle θ 2 , the ratio of θ 2 θ 1 is

A simple pendulum oscillates in a vertical plane. When it passes through the bottommost point, the tension in the string is 3 times the weight of the pendulum bob. What is the maximum displacement of the pendulum of the string with respect to the vertical?

A bullet of mass m moving with a horizontal velocity u strikes a stationary wooden block of mass M suspended by a string of length L = 50 cm. The bullet emerges out of the block with speed u 4 . If M = 6 m, the minimum value of u, so that the block can complete the vertical circle, is (Take, θ = 10 m s – 2 )

A flywheel gains a speed of 540 rpm in 6 second. Its angular acceleration will be

A small object placed on a rotating horizontal turn-table just slips when it is placed at a distance of 4 cm from the axis of rotation. If the angular velocity of the turn-table is doubled then the object slips when its distance from the axis of rotation is

A body is describing a circle of radius ‘r’. If the centripetal acceleration varies inversely with the square of the radius ‘r’, how does its velocity vary with the radius ?

A 1 kg stone at the end of 1 m long string is whirled in a vertical circle at constant speed of 4 m/sec. The tension in the string is 6 N when the stone is at (g,= 10 m/sec 2 )

Two bodies of masses 10 kg and 5 kg moving in concentric orbits of radii R and r such that their periods are the same. Then the ratio between their centripetal accelerations is

A particle is moving along a circular path of radius 5 m and with uniform speed 5 m/s. What will be the average acceleration when the particle completes half revolution

If v = ( 5 gl ) , what will be the velocity of the bob at the top of vertical circle

A mass m is revolving in a vertical circle at the end of a string of length 20 cm. By how much does the tension of the string at the lowest point exceed the tension at the top most point?

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

A vehicle is moving with a velocity v on a curved road of width b and radius of curvature R. For counteracting the centrifugal force on the vehicle, the difference in elevation required in between the outer and inner edges of the road is

A can filled with water is revolved in a vertical circle of radius 4 metre and the water just does not fall down. The time period of revolution will be

A car is moving in a circular horizontal track of radius 10 m with a constant speed of 10 m/s. A plumb bob is suspended from the roof of the car by a light rigid rod of length 1.00 m. The angle made by the rod with the track is

The string of a pendulum of length l is displaced through 90 o from the vertical and released. Then the minimum strength of the string in order to withstand the tension as the pendulum passes through the mean position is

The slope of the smooth banked horizontal road is p. If the radius of curve be r, then the maximum velocity with which a car can negotiate the curve is given by

A smooth block is released at rest on a 45° incline and then slides a distance d. The time taken to slide is n times as much to slide on rough incline than on a smooth incline. The coefficient of friction is

For traffic moving at 60 km/ hour along a circular track of radius 0⋅1 km, the correct angle of banking is

A stone tied to a string is rotated with a uniform speed in a vertical plane. If mass of the stone is m, length of the string is r and linear speed of the stone is v, then tension in the string when the stone is at its lower point is ( g = acceleration due to gravity)

A particle moves along a circle of radius 20 Ï m with constant tangential acceleration. It the velocity of the particle is 80 m/s at the end of the second revolution after motion has begun, the tangential acceleration is

A can filled with water is revolved in a vertical circle of radius 4 metre and the water just does not fall down. The time period of revolution will be

A particle of mass 10 g moves along a circle of radius 6 . 4 c m with a constant tangential acceleration. What is the magnitude of this acceleration if the kinetic energy of the particle becomes equal to 8 × 10 – 4 J by the end of the second revolution after the beginning of the motion?

A car is negotiating a curved road of radius R . The road is banked at an angle θ . The coefficient of friction between the tyres of the car and the road is μ s . The maximum safe velocity on this road is

A pendulum is oscillating in a vertical plane. The acceleration at the extreme position and lowest position are equal. Then the angular amplitude of the pendulum is

A mass m is attached to a thin wire and whirled in a vertical circle. The wire is most likely to break when

Six similar bulbs are connected as shown in the figure with a DC source of emf E, and zero internal resistance. The ratio of power consumption by the bulbs when (i) all are glowing and (ii) in the situation when two from section A and one from section B are glowing, will be

Two particles A and B are moving in uniform circular motion in concentric circles of radii r A and r B with speed v A and v B respectively. Their time period of rotation is the same. The ratio of angular speed of A to that of B will be

Two stones of masses m and 2 m are whirled in horizontal circles, the heavier one in a radius r 2 and the lighter one in radius r. The tangential speed of lighter stone is n times that of the value of heavier stone when they experience same centripetal forces. The value of n is

The position vector of a particle R as a function of time is given by R = 4 sin ( 2 π t ) i ^ + 4 cos ( 2 π t ) j ^ Where R is in meters, t is in seconds and i ^ and j ^ denote unit vectors along x-and y-directions, respectively. Which one of the following statements is wrong for the motion of particle?

In the given figure, 15 m s – 2 represents the total acceleration of a particle moving in the clockwise direction in a circle of radius R = 2.5 m at a given instant of time. The speed of the particle is

A car is moving in a circular horizontal track of radius 10 m with a constant speed of 10 m / s. A bob is suspended from the roof of the car by a light wire of length 1.0 m. The angle made by the wire with the vertical is

One end of string of length l is connected to a particle of mass ‘m’ and the other end is connected to a small peg on a smooth horizontal table. If the particle moves in circle with speed ‘v’, the net force on the particle (directed towards centre) will be (T represents the tension in the string)

A plano-convex lens of unknown material and unknown focal length is given. With the help of a spherometer we can measure the,

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

A body tied with string of length l and rotates in a vertical circle. If the maximum tension is two times the minimum tension then the minimum speed of the body is

A particle starting from rest, moves in a circle of radius ‘r’. It attains a velocity of V 0 m/s in the n th round. Its angular acceleration will be,

A particle is moving along a circular path of radius 6 m with a uniform speed of 8 m/s. The average acceleration when the particle complete one half of the revolution is

A pendulum bob has a mass m = 1 2 k g and length of string l = 1 m . The bob is released from position A. Then maximum tension in the string is

A uniform rod of length 1 m and mass 2 kg rotates in a horizontal plane at an angular speed of 6 rad/s, about an axis perpendicular to its length and passing through one of its ends. Then the tension induced at its mid-point is

Two bodies of masses m and 4m are attached to a light string as shown in Fig. A body of mass m hanging from string is executing oscillations with angular amplitude 60°, while other body is at rest on a horizontal surface. The minimum coefficient of friction between mass Am and the horizontal surface is (here pulley is light and smooth)

Two wheels having radii in the ratio 1 : 3 are connected by a common belt. If the smaller wheel is accelerated from rest at a rate d f 1 . 5 r a d / s 2 for 10 s. Find the angular velocity of bigger wheel.

A coin is placed at the edge of a horizontal disc rotating about a vertical axis through its axis with a uniform angular speed 2 rad s – 1 . The radius of the disc is 50 cm. Find the minimum coefficient of friction between disc and coin so that the coin does not slip (g = 10 m s – 2 ).

A small sphere of mass m is tied to one end of a string of length l. The other end of the string is attached to a fixed point o . The sphere is released from position A when the string is horizontal and the sphere starts moving in a vertical circle. When the string makes an angle of θ with horizontal, centripetal acceleration of the sphere is,

A particle moves with constant speed along a circular path of radius 1m. Time period of revolution of the particle is 2 sec. Then magnitude of average velocity of the particle when it moves from one point to the diametrically opposite point is

One end of a light string of length l is tied to a small sphere and the other end is attached to a fixed point O at the ceiling of a room. The sphere is gently released from rest when the string is horizontal. When the string is vertical, acceleration of the sphere is

A frictionless track ABCDE ends in a circular loop of radius R. A body slides down the track from point A which is at height h=5 cm. Maximum value of R for a body to complete the loop successfully is

A particle is moving in a circular path of radius 1m with a uniform speed of 1m/s. What is its average acceleration during the journey from A to B?

A simple pendulum crosses the highest point of a vertical circle with critical speed. What will be the centripetal acceleration of the bob, when the string is horizontal?

Centripetal acceleration is

Velocity vector and acceleration vector in a uniform circular motion are related as

When milk is churned, cream gets seperated due to

A particle revolves around a circular path. The acceleration of the particle is inversely proportional to

Two particles having mass M and m are moving in a circular path having radius R and r. If their time period are same then the ratio of angular velocity will be

A particle moves on a circle of radius r with centripetal acceleration as function of time as a e = k 2 rt 2 where k is a positive constant. Find the resultant acceleration.

A particle is moving along a circular path in xy-plane. When it crosses x-axis, it has an acceleration along the path of 1.5 m/s 2 , and is moving with a speed of 10m/s in -ve y – direction. The total acceleration is

A particle moves in a circular path such that its speed v varies with distance as v = α√s where is a positive constant. Find the acceleration of particle after traversing a distance S?

A cyclist is riding with a speed of 27kmh –1 . As he approaches a circular turn on the road of radius 80m, he applies brakes and reduces his speed at the constant rate of 0.50ms –1 every second. The net acceleration of the cyclist on the circular turn is

A body is moving in a circular orbit. It is just about to slide to the outer side and µ mg = mv 2 / r . In this expression, µ represents

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

A vehicle is travelling along unbanked curved path. If the friction between the road and tyres suddenly disappears then the vehicle

A car moves along a horizontal circular road of radius r with velocity v .The coefficient of friction between the wheels and the road is . Which of the following statement is not true?

A body moves along a circular path of radius 5m. The coefficient of friction between the surface of the path and body is 0.5. The maximum angular velocity in radian s –1 with which the body should move so that it does not leave the path is (g=10ms –2 )

A car is driven round a curved path of radius 18m without the danger of skidding. The coefficient of friction between the tyres of the car and the surface of the curved path is 0.2. What is the maximum speed in kmph of the car for safe driving ? (g = 10ms –2 )

A coin is kept at distance of 10 cm from the centre of a circular turn table. If µ = 0.8 , the frequency of rotation at which the coin just begins to slip is

The centripetal force required by a 1000 kg car that takes a turn of radius 50 m at a speed of 36 kmph is

A curved section of a road is banked for a speed v .If there is no friction between the road and the tyres then

A block of mass 10 kg is in contact against the inner wall of a hollow cylindrical drum of radius 1m. The coefficient of friction between the block and the inner wall of the cylinder is 0.1. The minimum angular velocity needed for the cylinder to keep the block stationary when the cylinder is vertical and rotating about is axis, will be

A cyclist moves along a curved road with a velocity v. The road is banked for speed v. The angle of banking is θ .Which of the following statements in not true?

A mass of 0.1 kg is rotated in a vertical circle using a string of length 20 cm. When the string makes an angle 30 o with the vertical, the speed of the mass is 1.5ms –1 . The tangential acceleration of the mass at that instant is

A 2 kg stone is swung in a vertical circle by attaching it at the end of a string of length 2m. If the string can with stand a tension 140.6N, the maximum speed with which the stone can be rotated is

A bob of mass 100 g tied at the end of a string of length 50 cm is revolved in a vertical circle with a constant speed of 1 ms –1 . When the tension in the string is 0.7N, the angle made by the string with the vertical is (g = 10 ms –2 ) .

A simple pendulum of length ‘l’ carries a bob of mass m. If the breaking strength of the string is 2 mg, the maximum angular amplitude from the vertical can be

A 1kg ball is rotated in a vertical circle by using a string of length 0.1 m. If the tension in the string at the lowest point is 29.4N, its angular velocity at that position is

A ball of mass ‘m’ is rotated in a vertical circle with constant speed. The difference in tensions at the bottom and horizontal positions would be

The velocity of a body revolving in a vertical circle of radius ‘r’ at the lowest point is √(7gr) . The ratio of maximum to minimum tensions in the string is

A small glass marble of mass ‘m’ oscillates between the two edges, inside a hemispherical glass bowl of radius ‘r’.If ‘V’ is the speed of marble at the lowest position, the normal reaction at that position is

A simple pendulum bob is given a horizontal velocity at the bottom. The string slackens after swinging through an angle θ with the vertical. The θ is

A mass of 2.9 kg is suspended from a string of length 50 cm and is at rest. Another body of mass 100 g which is moving horizontally with a velocity of 150 m/s strikes and sticks to it subsequently when the string makes an angle of 60 o with the vertical, the tension in the string is (g=10m/s 2 )

A particle of mass 2 kg is moving in a circular path of radius 1 m. Speed of the particle is increasing at a rate 1 m / s 2 . Then the force acting on the particle when its speed is 1 m / s is

A car moving at 18 kmph tries to round a corner in a circular arc of 8 m radius on flat roadway. How large must be the coefficient of friction between wheels and roadway if the car is not to skid?

A particle is moving in the vertical plane. It is attached at one end of a string of length l whose other end is fixed. The velocity at the lowest point is u. The tension in the string is T and velocity of the particle is v at any position. Then, which of the following quantity will remain constant.

A car is negotiating a curved road of mean radius R. The surface of the road is frictionless and it makes an angle θ with horizontal. Then the necessary centripetal force is supplied by the

A particle starts from rest and moves along a circular path of radius 5m with a tangential acceleration of constant magnitude. If the length of path traversed by the particle in 2 second is 20 m, its angular acceleration is

A car moving with sped 10 m/s along a circular road of mean radius 50 m. The surface of the road is horizontal. What must be the minimum coefficient of friction between the road surface and tyres to avoid skidding?

A particle is moving in a circular path of constant radius with constant speed of 4 m/s and constant angular velocity of 5 rad/sec. Then magnitude of its centripetal acceleration is

The length of a simple pendulum is 1m. The bob is given a velocity 7m/s in horizontal direction from mean position. During upward motion of bob, if the string is burnt when it is horizontal, then the maximum vertical height of ascent of bob from rest position is

A string of length L is fixed at one end and carries a mass M at the other end. The string makes 2 π revolutions per second around the vertical axis through the fixed end as shown in the figure, then tension in the string is

Three masses of small size are attached by light inextensible strings of various lengths to a point O on the ceiling. All of the masses swing round in horizontal circles of various radii with the same angular frequency ω (one such circle is drawn in the shown figure.) Then pick up the correct statement.

Two particles tied to different strings are whirled in a horizontal circle as shown in figure. The ratio of lengths of the strings so that they complete their circular path with equal time period is:

A pendulum of length / = l m is released from θ 0 = 60 0 . The rate of change of speed of the bob at θ = 30 0 is (g = 10 m / s 2 )

A truck is carrying a box of mass m = 50 kg on its flat horizontal rough surface with coefficient of friction μ = 0.3. It is crossing a circular track of radius 27 m. What is the maximum speed of the truck so that the box does not slide from the truck while moving on the circular path?

A heavy particle hanging from a string of length l is projected horizontally with speed gl . The speed of the particle at the point where the tension in the string equals weight of the particle is

A particle originally at rest at the highest point of a smooth vertical circle is slightly displaced. It will leave the circle at a vertical distance h below the highest point, such that h is equal to

A particle is moving with a velocity of v = ( 3 i ^ + 4 t j ^ ) m/s. Find the ratio of tangential acceleration to that of normal acceleration at t= 1sec.

A tube of length L is filled completely with an incompressible liquid of mass M and closed at both the ends. The tube is then rotated in a horizontal plane about one of its ends with a uniform angular velocity ω . The force exerted by the liquid at the other ends is :

The angular displacement of a particle is given by θ = t 3 + 2 t + 1 where t is time in seconds. Its angular acceleration at t = 2s is

A circular disc is rotating about its own axis at a uniform angular velocity ω The disc is subjected to uniform angular retardation by which its angular velocity is decreased to ω 2 during 120 rotations. The number of rotations further made by it before coming to rest is

The whole set up shown in the figure where particles ( m 1 and m 2 are) rotating with constant angular velocity w on a horizontal frictionless table. If T 1 and T 2 are tension in given strings then ratio of tensions T 1 /T 2 is:

A cyclist riding the bicycle at a speed of 14 3 ms − 1 takes a turn around a circular road of radius 20 3 m without skidding. Given g= 9.8 m/s 2 , what is his inclination to the vertical.

Choose the incorrect statement:

As the motorcycle moving with a constant velocity ascenda on the overbridge of R, then the normal force on it,

A car of mass 1000 kg negotiates a banked curve of radius 90 m on a frictionless road. If the banking angle is 45 o , the speed of the car is

A car of mass m is moving on a level circular track of radius R. If μ s represents the coefficient of static friction between the road and tyres of the car, the maximum speed of the car in circular motion is given by:

The centripetal force required for a 1000 kg car travelling at 36 kmph to take a turn by 90° in travelling along an arc of length 628 m is

A car is travelling along a curved road of radius r. If the coefficient of friction between the tyres and the road is μ , the car will skid if its speed exceeds

A disc rotates at 60 rev/min around a vertical axis. A body lies on the disc at the distance of 20cm from the axis of rotation. What should be the minimum value of coefficient of friction between the body and the disc, so that the body will not slide off the disc

The angular velocity of a particle moving in a circle of radius 50 cm is increased in 5 min from 100 revolutions per minute to 400 revolutions per minute. Find the tangential acceleration of the particle.

A particle moves, so that its position vector is given by r = cosω t x ^ + sinω t y ^ , where ω is a constant. Which of the following is true?

A body is hanging from a rigid support by an inextensible string of length I . It is struck inelastically by an identical body of mass m with horizontal velocity v = 2 g l , the tension in the string increases just after striking by {AFMC 2012]

The speed of a particle moving in a circle is increasing. The dot product of its acceleration and velocity is

A bucket full of water is rotated in a vertical circle of radius R. If the water does not split out, the speed of the bucket at topmost point will be

An unbanked curve has a radius of 60 m. The maximum speed at which a car can make a tum, if the coefficient of static friction is 0.75, is

A car is moving on a circular path and takes a tum. If R 1 and R 2 be the reactions on the inner and outer wheels respectively, then

A particle of mass m is circulating on a circle of radius r having angular momentum L about centre. Then, the centripetal force will be

A body of mass 1 kg is moving in a vertical circular path of radius 1 m. The difference between the kinetic energies at its highest and lowest positions is

A fan makes 2400 rpm. If after it is switched off, it comes to rest in 10 s, then find the number of times it will rotate before it comes to rest after it is switched off.

A circular curve of a highway is designed for traffic moving at 72 kmh -1 . If the radius of the curved path is 100 m, the correct angle of banking of the road should be

A train has to negotiate a curve of radius 800 m. By how much height should the outer rail be raised with respect to inner rail for a speed of 96 kmh -1 ? The distance between the rails is 1 m.

If the banking angle of curved road is given by tan – 1 3 5 and the radius of curvature of the road is 6 m, then the safe driving speed should not exceed (Take, g = 10 ms -2 )

A motorcyclist moving with a velocity of 144 kmh -1 on a flat road takes a turn on the road at a point, where the radius of curvature of the road is 40 m. The acceleration due to gravity is 10 ms -2 . In order to avoid sliding, he must bend with respect to the vertical plane by an angle

An automobile enters a turn of radius R. If the road is banked at an angle of 45 0 and the coefficient of friction is 1, the minimum speed with which the automobile can negotiate the turn without skidding is

A stone is rotated in a vertical circle. Speed at bottommost point is 8 g R where R is the radius of circle. The ratio of tension at the top and the bottom is

When the angular velocity of a uniformly rotating body has increased thrice, the resultant of forces applied to it increases by 60 N. Find the accelerations of the body in the two cases. The mass of the body m = 3 kg.

A simple pendulum of length I has a maximum angular displacement θ . The maximum kinetic energy of the bob of mass m will be

A stone of mass 1 kg tied to a light inextensible string of length L = 10 3 m, whirling in a circular path in a vertical plane. The ratio of maximum tension to the minimum tension in the string is 4. If g is taken to be 10 m s – 2 , the speed of the stone at the highest point of the circle is

A particle of mass m is fixed to one end of light spring of force constant k and unstretched length I as shown in fig. (5). The system is rotated about the other end of the spring with angular velocity o in gravity free space. The increase in length of the spring will be

A car turns a corner on a slippery road at a constant speed of 12 m/s. If the coefficient of friction is 0.4, the minimum radius of the arc in metre in which the car turns is

A pendulum consists of a wooden bob of mass m and length I . A bullet of mass m 1 is fired towards the pendulum with a speed v 1 . The bullet emerges out of the bob with a speed v 1 3 , and the bob completes a motion along a vertical circle. then v 1 is

A body moves along circular path of radius 10 m and the coefficient of friction is 0 5. What should be its angular velocity in rad,/sec if it is not to slip from the surface. g = 9.8 m/s 2 .

A hemispherical bowl of radius R is set rotating about its axis of symmetry. A small body kept in the bowl rotates with the bowl without slipping on its surface. If radius through the body makes with the axis an angle θ . θ and assuming that the surface of the bowl is smooth, the angular velocity with which bowl is rotating is given by

An annular ring with inner and outer radii R 1 , and R 2 , is rolling without slipping with a uniform angular speed. The ratio of the forces experienced by the two particles situated on the inner and outer parts of the ring F 1 /F 2 , is

A coin is placed on a horizontal platform which undergoes vertical simple harmonic motion of angular frequency ω The amplitude of oscillation is gradually increased. The coin will leave contact with the platform for the first time

Directions : These questions consist of two statements each printed as Assertion and Reason. While answering these questions you are required to choose any one of the following four responses Assertion: One end of a massless rod of length l is hinged, so that it is free to rotate in a vertical plane about a horizontal axis. If a particle is attached to the other end of the rod, then the minimum speed at lower most position of the particle is 5 g l to complete the circular motion. Reason : Work done by centripetal force on the particle is always zero.

Which of the following statement(s) is/are correct? I. When a bucket containing water is whirled fast overhead, the water does not fall out at the top of the circular path. II. The centripetal force in this position on water is more than the weight of water.

A particle undergoes uniform circular motion on a horizontal xy plane. At time t = 0, it moves through coordinates (3.0 m, 0) with velocity v = 6 .0 m / s j ^ . At t = 5.0 s, it moves through (11.0 m, 0) with velocity v = − 6 .0 m / s j ^ . What is its acceleration at t = 2.5 s?

A rotating wheel changes angular speed from 1800 rpm to 3000 rpm in 20 s. What is the angular acceleration assuming to be uniform? [KCET 2014]

A stone tied to a rope is rotated in a vertical circle with uniform speed. If the difference between the maximum and minimum tensions in the rope is 20 N, mass of the stone (in kg) is (Take, 9 = 10 m s – 2 ) [EAMCET 2013]

A particle rests on the top of a hemisphere of radius R. Find the smallest horizontal velocity that must be imparted to the particle if it is to leave the hemisphere without sliding down it

A small body of mass m slides down from the top of a hemisphere or radius r (Fig. 2). The surface of block and hemisphere are frictionless. The height at which the body lose contact with the surface of the sphere is

A body of mass m kg is rotating in a vertical circle at the end of a string of length r metre. The difference in the kinetic energy at the top and the bottom of the circle is

Keeping the banking angle same, to increase the maximum speed with which a vehicle can travel on the curved road by 10%, the radius of curvature of the road has to be changed from 20 m to

A string of length l = 1 m is fixed at one end and carries a mass of 100gm at other end. The string makes 5 / π revolutions per second about a vertical axis passing through its second end. What is the angle of inclination of the string with the vertical ? Take g = 10 m/s 2

A simple pendulum is oscillating with an angular amplitude of 90 o as shown in fig. (4). The value of θ for which the resultant acceleration of the bob is directed horizontally is

The maximum speed that can be achieved without skidding by a car on a circular unbanked road of radius R and coefficient of kinetic friction μ is

A bob of mass m is attached to one end of a string of length l . This is kept in the horizontal position and released from the rest. At what angle from vertical will the tension in the string be equal to the weight in magnitude ?

A small block is placed at the top of a sphere. It slides on the smooth surface of the sphere. What will be the angle made by the radius vector of the block with the horizontal when it leaves the surface ?

A curved road of 50 m in radius is banked to correct angle for a given speed. If the speed is to be doubled keeping the same banking angle, the radius of curvature of the road should be changed to

A particle of mass m slides from rest from position A, along a smooth circular track of radius R as shown in fig. (7a). The vertical distance travelled by m before leaving the surface of the track is

For traffic moving at 60 km/hr along a circular track of radius 0â
1 km, the correct angle of banking is

A stone is tied to a string of length ‘ l ‘ and is whirled in a vertical circle with the other end of the string as the centre. At a certain instant of time, the stone is at its lowest position and has a speed ‘u’. The magnitude of the change in velocity as it reaches a position where the string is horizontal ( g being acceleration due to gravity) is

A stone tied to the end of a string of 1 m long is whirled in a horizontal circle with a constant speed. If the stone makes 22 revolutions in 44 sec, what is the magnitude and direction of acceleration of the stone ?

For traffic moving at 60 km/ hour along a circular track of radius 0⋅1 km, the correct angle of banking is

A simple pendulum consists of light string from which a spherical bob of mass m is suspended. The distance between the point of suspension and the centre of the bob is l . The bob is given a tangential velocity v at the position of equilibrium (bottom). What can be maximum value of V so that the pendulum oscillates without the string becoming slack?

The angular speed of the wheel of a vehicle is increased from 360 rpm to 1200 rpm in 14 s. Its angular acceleration is [NEET 2020]

If a disc starting from rest acquires an angular velocity of 240 rev min -1 in 10s, then its angular acceleration will be [BCECE (Mains) 2012] (a)4.26 rad/ s – 2 (b) 3.11 rad s-2 (c) 2.51 rad s-2 (d) 1.13 rad S-2

A particle is moving in a circular orbit with constant speed. Choose the incorrect statement.

If an object starts from rest and covers angle of 60 rad in 10s in circular motion, then magnitude of its angular acceleration will be [JIPMER 2019]

A particle travels in a circle of radius 20 cm at a uniformly increasing speed. If the speed changes from 8 ms – 1 to 9 ms – 1 in 2 s , what would be the angular acceleration (in rad s – 2 )? [UK PMT 2015]

A vehicle is moving with uniform speed along horizontal, concave and convex surface roads. The surface on which, the normal reaction on the vehicle is maximum is

A point size mass 100 gm is rotated in a vertical circle using a cord of length 20cm. When the string makes an angle 60° with the vertical, the speed of the mass is 1.5m/s. The tangential accelaration of the mass in that position is……..ms -2

A particle of mass m is moving in a circular path of constant radius r such that its centripetal acceleration a c is varying with time to as a c = k 2 rt 2 where k is a constant. What is the power delivered to the particle by the forces acting

A body moves along a circular path of radius 10 m and the coefficient of friction is 0.5. What should be its angular speed in rad/s if it is not to slip from the surface g = 9 .8 ms 2

A body moves along a circular path of radius 10 m and the coefficient of friction is 0.5. What should be its angular speed in rad/s if it not to slip from the surface g = 9 .8 ms 2

The maximum and minimum tensions in the string used to rotate a body in a vertical circle are in the ratio 19:1. The ratio of maximum to minimum speeds of the body

A vehicle is travelling with uniform speed along a concave road of radius of curvature 19.6 m. At lowest point of concave road if the normal reaction on the vehicle is three times its weight, the speed of vehicle is …….ms -1