For JEE Main other Engineering Entrance Exam Preparation, **JEE Main Physics Laws of Motion** PYQ’s with Solutions is given below.

**Multiple Choice with ONE correct answer**

**1.A ship of mass 3 x 10 ^{7} kg initially at rest is pulled by a force of 5 x 10^{4} N through a distance of 3m. Assuming that the resistance due to water is negligible, the speed of the ship is [1980-2 marks]**

**a) 1.5m/s b) 60 m/s**

**c) 0.1 m/s d) 5 m/s**

**Ans.**

**2.A block of mass 2kg rests on a rough inclined plane making an angle of 30° with the horizontal. The co-efficient of static friction between the block and the plane is 0.7. The frictional force on the block is [1980-2 marks]**

**Ans.**

**3.In the arrangement, shown in the figure, the ends P and Q of an unstretchable string move downwards with uniform speed u. Pulleys A and B are fixed. Mass M moves upwards with a speed [1982-3 marks]**

**Ans.**

**4.During peddling of a bicycle, the force of friction exerted by the ground on the two wheels is such that it acts [1990-2 marks]**

** a)in the backward direction on the front wheel and in the forward direction on the rear wheel**

** b)in the forward direction on the front wheel and in the backward direction on the rear wheel**

** c)in the backward direction on both, the front and the rear wheels**

** d)in the forward direction on both, the front and the rear wheels.**

**Ans.**(a) due to peddling, the point of contact of real wheel has a tendency to move backwards. So frictional force opposes the back ward tendency i,e., frictional force acts in the forward direction. But the back wheel accelerates the front wheel in the forward direction. To oppose this frictional force acts in the back ward direction on front wheel.

**5.A car is moving in a circular horizontal track of radius 10m with a constant speed of lOm/s. A plumb bob is suspended from the roof of the car by a light rigid rod. The angle made by the rod with the track is (g = 10 m/s ^{2}) [1992-2 marks]**

**a) zero b) 30° c) 45° d) 60°**

**Ans.**

**6.A block of mass 0.1 kg is held against a wall applying a horizontal force of 5N on the block. If the coefficient of friction between the block and the wall is 0.5, the magnitude of the frictional force acting on the block is [1994-1 mark]**

** a) 2.5N b) 0.98N c) 4.9N d) 0.49N**

**Ans.**

**Ans.**

**8.A small block is shot into each of the four tracks as shown below. Each of the tracks rises to the same height. The speed with which the block enters the track is the same in all cases. At the highest point of the track, the normal reaction is maximum in [2001-2 marks]**

**Ans.**

**9.An insect crawls up a hemispherical surface very slowly (see fig.) The coefficient of friction between the insect and the surface is 1/3.If the line joining the center of the hemispherical surface to the insect makes an angle alpha with the vertical the maximum possible value of alpha is given by [2001-1 mark]**

**Ans.**

a) 0° b) 30° c) 45° d) 60°

**Ans.**

**11.A string of negligible mass going over a clamped pulley of mass m supports a block of mass M as shown in the figure. The force on the pulley by the clamp is given by[2001-2 marks]**

**Ans.**

**12.What is the maximum value of the force F such that the block shown in the arrangement, does not move ? (g = 10ms ^{-2}) [2003-2 marks]**

**a) 20N**

**b)10N**

**c)12N**

**d)15N**

**Ans.**

**13.A block P of mass m is placed on a horizontal frictionless plane. A second block of same mass m is placed on it and is connected to a spring of spring constant k. The two blocks are pulled by distance A. Block Q oscillates without slipping. What is the maximum value of frictional force between the two blocks? [2004-2 marks]**

**Ans.**

**14.A blook of mass m is at rest under the action of force F against a wall as shown in the figure. Which of the following statements is incorrect ?[2005-2 marks]**

** a)f = mg [where f is frictional force]**

** b)F = N [Where N is normal force]**

** c)F will not produce torque**

** d)N will not produce torque.**

**Ans.**

**15.Two blocks A and B of masses 2m and m, respectively are connected by a massless and inextensible string.The whole system is suspended by a massless spring as shown in the figure.The magnitudes of acceleration of A and B, immediately after the string is cut, are respectively [2006-3 marks]**

** a) g, g/2 b) g/2, g c) g, g d) g/2, g/2**

**Ans.**

**16.Two particles of mass m each are tied at the., ends of a light string of length 2a. The whole system is kept on a frictionless ‘ a ‘ a horizontal surface with the string held tight so that each mass is at a distance a from the center P (as shown in the figure). Now, the mid-point of the string is pulled vertically upwards with a small but constant force F. As a result, the particles move towards each other on the surface. The magnitude of acceleration, when the separation between them [2007-3 marks]**

**Ans.**

a) 0° b) 30° c) 45° d) 90°

**Ans.**

**Ans.**

**19.If the resultant of all the external forces acting on a system of particles is zero, then from an inertial frame, one can surely say that [2009]**

** a)linear momentum of the system does not change in time**

** b)kinetic energy of the system does not change in time**

** c)angular momentum of the system does not change in time**

** d)potential energy of the system does not change in time**

**Ans.**(a) Linear momentum remains constant if net external force on the system of parlicle is zero.

**Ans.**

**21.A piece of wire is bent in the shape of a parabola y = kx ^{2} (y-axis vertical) with a bead of mass m on it. The bead can slide on the wire without friction. It stays at the lowest point of the parabola when the wire is at rest. The wire is now accelerated parallel to the x-axis with a constant acceleration a. The distance of the new equilibrium position of the bead, where the bead can stay at rest with respect to the wire, from the y-axis is [2009]**

**Ans.**

**Multiple Choice with ONE or More Than ONE correct answers**

**22.A reference frame attached to the earth [1986-2 marks]**

** a)is an inertial frame by definition.**

** b)cannot be an inertial frame because the earth is revolving round the sun.**

** c)is an inertial frame because Newton’s laws are applicable in this frame.**

** d)cannot be an inertial frame because the earth is rotating about its own axis.**

**Ans.**(b), (d) a) It is incorrect. Earth is an accelerated frame, obviously it cannot be an inertial frame.

b)It is correct

c)It is incorrect

Newton’s laws are applicable to it only as a limiting case.

d)It is correct

Infact, a rotating or a revolving frame is accelerating and hence non-inertial. Options (b) and (d) are correct.

**Assertion & Reasoning type**

**Instructions** : Each question contains statement-1(Assertion) and statement – 2 (Reason). Of these

statements, mark correct choice if

a)Statement-1 and 2 are true and statement-2 is a correct explanation for statement-1

b)Statement-1 and 2 are true and statement-2 is not a correct explanation for statement-1

c)Statement-1 is true, statement-2 is flase

d)Statement-1 is false, statement-2 is true.

**Ans.**

**23.Statement-1: A block of mass m starts moving on a rough horizontal surface with a velocity v. It stops due to friction between the block and the surface after moving through a certain distance. The surface is now tilted to an angle of 30°with the horizontal and the same block is made to go up on the surface with the same initial velocity v. The decrease in the mechanical energy in the second situation is smaller than that in the first situation.**

** Statement-2 :The coefficient of friction between the block and the surface decreases with the increase in the angle of inclination. [2007-3 marks]**

**Ans.**(c) You need to be clever. Do not waste time on statement-1, statement-2, is false. And only in alternative (c), the statement -2 is false.

**24.Statement-1 : A cloth covers a table. Some dishes are kept on it. The cloth can be pulled out without dislodging the dishes from the table.**

** Statement-2 :For every action, there is an equal and opposite reaction. [2007-3 marks]**

**Ans.**(b) The dishes will remain over there, their state of motion will not change, If the friction on them is not enough to change the state of motion as fast as that of the cloth.

**25.Statement-1 : For an observer looking out through the window of a fast moving train, the nearby objects appear to move in the opposite direction to the train, while the distant objects appear to be stationary.**

**Ans.**(b) Statement-1 relates to visual experience. Statement -2 is also correct. It is just the method the relative velocity of an object w.r.t another is calculated. But it does not explains Statement-1. The correct explanation of Statement-1 is passed on the visual perception of motion, particularly the angular velocity. The object appears to be moving faster when its angular velocity is greater.

**26.Statement-1 :It is easier to pull a heavy object than to push it on a level ground.**

** Statement-2 :The magnitude of frictional force depends on the nature of the two surfaces in contact.**

**Ans.**(b) Statement-1 is practical experience of everyday life, it is true.Statement-2 is also true but is not the correct explanation of Statement -1. Correct explanation of statement-1 is “ there is an increase in the normal reaction when the object is pushed and there is a decrease in the normal reaction when object is pulled”.

**Subjective / Numerical integer type**

**27.In the figure, the blocks A, B and C have masses 3kg, 4 kg and 8 kg respectively. The coefficient of sliding friction between any two surfaces is 0.25.A is held at rest by a massless rigid rod fixed to the wall, while B and C are connected by a light flexible cord passing around a fixed frictionless pulley. Find the force F necessary to drag C along the horizontal surface to the left at a constant speed. Assume that the arrangement shown in the figure, i.e, B on C and A on B, is maintained throughout.[1978]**

**Ans.**When block C is moved to the left, the block B will move to right (due to reaction of C on B) while block A always remains at rest. Let T be the tension in the cord when blocks Band C move. The frictional forces between the different surfaces are as follows.

**28.A uniform rope of length L and mass M is pulled by a constant force F. What is the tension in the rope at a distance l from the end where the force is applied? [1978]**

**Ans.**

**Ans**.(a) Refer the figure. When the block moves down the inclined plane, the force of friciton f acts upwards along the plane. Let Fj be the force needed to make the block move without any acceleration. As the acceleration is zero, no net force acts on the block as its slides down the plane. Hence

**30.Two blocks connected by a massless string slide do\frn an inclined plane having an angle of inclination of 37°. The masses of the two blocks are M! – 4kg and M _{2} = 2kg respectively and the coefficients of friction of Mj and M_{2} with the inclined plane are 0.75 and 0.25 respectively Assuming the string to be taut, find (i) the common acceleration of two masses and (ii) the tension in the string.**

**(sin 37° = 0.6, cos37° = 0.8) [Takeg = 9.8ms**

^{-2}]**Ans.**

**31.Masses M _{p} M_{2} and M_{3} are connected by strings of negligible mass which pass ^{Ml }over massless and frictionless pulleys Pj and P_{2} as shown in the figure. The masses move such that the portion of the string between Pj and P_{2} is parallel to the inclined plane and the portion of the string between P_{2} and M_{3} is horizontal. The masses M_{2} and M_{3} are 4.0kg each and the co-efficient of kinetic friction between the masses and the Surfaces is 0.25. The inclined plane makes an angle of 37° with the horizontal. If the mass Mj moves downwards with a uniform velocity, find**

**i)The mass of**

**ii)The tension in the horizontal portion of the string**

**(g = 9.8m/sec**

^{2}, sin37° =3/5) [1981-6 marks]**Ans.**The question gives that mass Mj moves downwards with a uniform velocity. It means that net acceleration of the system is zero. It is possible if the net pulling force, due to weights of M,, M

_{2}& M

_{3}and frictional force, is zero.

**32.A particle of mass m rests on a horizontal floor with which it has a co-efficient of static friction (X. It is desired to make the body move by applying the minimum possible force F. Find the magnitude of F and the direction in which it has to be applied. [1987-7 marks]**

**Ans.**

**33.Two blocks of mass 2.9 kg and 1.9 kg are suspended from a rigid support S by two inexten- sible wires each of length 1 meter, see figure. The upper wire has negligible mass and the lower wire has a uniform mass of 0.2kg/m.The whole system of blocks, wires and support have an upward acceleration of 0.2 m/s ^{2}. Acceleration due to gravity is 9.8 m/s^{2}[1989-6 marks]**

**i) Find the tension at the mid-point of the lower wire.**

**ii) Find the tension at the mid-point of the upper wire.**

**Ans.**

**Ans.**

**35.A smooth semic ircular wire- track of radius R is fixed in a vertical plane. One end of a massless spring of natural length 3R/4 is attached to the lowest point O of the wire- track. A small ring of mass m, which can slide on the track, is attached to the other end of the spring. The ring is held stationary at point P such that the spring makes an angle of 60° with the vertical. The spring constant K=mg/R. Consider the instant when the ring is released, and**

** i)draw the free body diagram of the ring,**

** ii)determine the tangential acceleration of the ring and the normal reaction.**

**Ans.**

**36.Block A of mass m and block B of mass 2m are placed on a fixed triangular wedge by means of a massless inexten- sible string and a frictionless pulley as shown in the figure. The wedge is inclined at 45° to the horizontal on both sides. The coefficient of friction between block A and the wedge is 2/3 and that between block B and the wedge is 1/3. If the system of A and B is released from rest, find (i) The acceleration of A, (ii) Tension in the string, & (iii) The magnitude and the direction of the force of friction acting on A. [1997-5 marks]**

**Ans.**

**37.Two blocks of mass m1 = 10kg and m _{2} = 5kg, connected to each other by a massless inextensible string of length 0.3m are placed along a diameter of a turn table. The co-efficient of friction between the table and nijis 0.5 while there is no friction between rr^ and the table. The table is rotating with an angular velocity of lOrad/s about a vertical axis passing through its centre O. The masses are placed along the diameter of the table on either side of the centre O such that the mass m1 is at a distance of 0.124m from O.The masses are observed to be at rest with respect to an observer on the turn table.[1997-5 marks]**

**a)Calculate the frictional force on m1**

**b)What should be the minimum angular speed of the turn table so that the masses will slip from this position?**

**c)How should the masses be placed with the string remaining taut, so that there is no frictional force acting on the mass m1?**

**Ans.**

**38.In the figure masses m1, m _{2} and M are 20 kg, 5 kg and 50 kg respectively. The co-efficient of friction between M and ground is zero. The co-efficient of friction between m1 and M and that between m_{2 }and ground is 0.3. The pulleys and the strings are massless. The string is perfectly horizontal between P, and m1 and also between P_{2} and m_{2} .The string is perfectly vertical between P, and P_{2}. An external horizontal force F is applied to the mass M. Take g = 10 m/s^{2}. [2000-10 marks]**

**(a)Draw a free-body diagram for mass M, clearly showing all the forces.**

**(b)Let the magnitude of the force of friction between m1 and M be f1 and that between m**

_{2}and ground be f_{2}. For a p articular F it is found that f1 = 2 f_{2}. Find f1 and f_{2}.Write equations of motion of all the masses Find F, tension in the string and acceleration of the masses.**Ans.**

**Ans.**

**Ans.**

**41.A light inextensible string that goes over a smooth fixed pulley as shown in the figure connects two blocks of masses 0.36 kg and 0.72 kg. Taking g = 10 m/s ^{2}, find the work done (in joules) by the string on the block of mass 0.36 kg during the first second after the system is relesed from rest.**

**Ans.**

**Ans.**

**True/ False Type**

**43.A rocket moves forward by pushing the surrounding air backwards. [1980]**

**Ans.**False:A rocket is propelled not by pushing the surrounding air backwards but by the ejection of a portion of its mass to the back. The forward force on the rocket is the reaction to the backward force on the ejected material and as more material is ejected, the mass of the rocket decreases.

**44. When a person walks on a rough surface, the frictional force exerted by the surface on the person is opposite to the direction of his motion.[1981-2 mark]**

**Ans.**False:When a person walks on a rough surface, he pushes the foot backward . The motion of the surface of contact is backward. Therefore the frictional force will act in the forward direction which is the direction of motion of the person, the statement is false.

**45.The pulley arrangements of figure (a) and (b) are identical. The mass of the rope is negligible. In (a) the mass m is lifted up by attaching a mass 2m to the other end of the rope. In (b), m is lifted up by pulling the other end of the rope with a constant downward force F = 2mg. The acceleration of m is the same in both cases. [1984-2 marks]**

**Ans.**

**Fill in the blanks**

**46.A block of mass 1kg lies on a horizontal surface in a truck. The coefficient of static friction between the block and the surface is 0.6. If the acceleration of the truck is 5 m/s ^{2}, the frictional force acting on the block is newton.[1984-2 marks]**

**Ans.**

**Ans.**