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JEE Center of Mass, Momentum and Collision PYQs with Solutions

358 previous year questions from Center of Mass, Momentum and Collision (JEE Main & Advanced Physics) with answers and solutions. Numbered list, year tags, and one-tap solutions — built for serious JEE / NEET practice.

358 questionsPhysics2002–2026Answers + solutions

About Center of Mass, Momentum and Collision PYQs

Center of Mass, Momentum and Collision has 358 previous year questions in the Quantrex Academy JEE Main & Advanced Physics bank. The 220 questions in this list come from JEE Main (130), NTA Abhyas JEE Main (70) and JEE Advanced (20), spanning 2002 to 2026. Each question opens on its own page with the options, the correct answer and the worked solution where available.

Questions by year (this list)

  • 2026: 7
  • 2025: 9
  • 2024: 13
  • 2023: 14
  • 2022: 13
  • 2021: 15
  • 2020: 89
  • 2019: 15
  • 2018: 4
  • 2017: 3
  • 2016: 1
  • 2015: 3

Center of Mass, Momentum and Collision questions with solutions

1

Two identical bodies A and B of equal masses have initial velocities v_1 = 4 i m/s and v_2 = 4 j m/s respectively. The body A has acceleration a_1 = 6 i + 6 j m/s ^2 while the

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2

The position of center of mass of three masses 2 kg, 3 kg and 15 kg placed with respect to mid point ( p ) of normal bisector, as shown in the figure is _______.

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3

Two blocks of masses 2 kg and 1 kg respectively, are tied to the ends of a string which passes over a light frictionless pulley as shown in the figure below. The masses are held

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4

The position of an object having mass 0.1 kg as a function of time t is given as r = (10t^2 i + 5t^3 j ) m. At t = 1 s, which of the following statements are correct ? A. The

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5

A body of mass 14 kg initially at rest explodes and breaks into three fragments of masses in the ratio 2: 2: 3 . The two pieces of equal masses fly off perpendicular to each other

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6

In a perfectly inelastic collision, two spheres made of the same material with masses 15 kg and 25 kg, moving in opposite directions with speeds of 10 ~m / s and 30 ~m / s

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7

Given below are two statements : Statement I : For a mechanical system of many particles total kinetic energy is the sum of kinetic energies of all the particles. Statement II

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8

In a scattering experiment, a particle of mass 2 m collides with another particle of mass m , which is initially at rest. Assuming the collision to be perfectly elastic, the

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9

A rod of length 5 L is bent right angle keeping one side length as 2 L. The position of the centre of mass of the system: (Consider L=10 ~cm )

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10

Consider two blocks A and B of masses m_1=10 ~kg and m_2=5 ~kg that are placed on a frictionless table. The block A moves with a constant speed v=3 ~m / s towards the block B kept

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11

Given below are two statements. One is labelled as Assertion (A) and the other is labelled as Reason (R). Assertion (A) : Three identical spheres of same mass undergo one

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12

As shown below, bob \(A\) of a pendulum having massless string of length ' \(R\) ' is released from \(60^ ∘ \) to the vertical. It hits another bob \(B\) of half the mass that is

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13

A uniform rod of mass 250 g having length 100 cm is balanced on a sharp edge at 40 cm mark. A mass of 400 g is suspended at 10 cm mark. To maintain the balance of the rod, the

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14

A balloon and its content having mass M is moving up with an acceleration ' a '. The mass that must be released from the content so that the balloon starts moving up with an

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15

The center of mass of a thin rectangular plate (fig - x ) with sides of length a and b , whose mass per unit area (σ) varies as σ=(σ_0 x)/(a b) (where σ_0 is a constant), would be

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16

Consider a circular disc of radius 20 cm with centre located at the origin. A circular hole of radius 5 cm is cut from this disc in such a way that the edge of the hole touches

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17

Paragraph II: Two particles, 1 and 2 , each of mass m , are connected by a massless spring, and are on a horizontal frictionless plane, as shown in the figure. Initially, the two

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18

Two particles, 1 and 2 , each of mass m , are connected by a massless spring, and are on a horizontal frictionless plane, as shown in the figure. Initially, the two particles

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19

Three bodies A, B and C have equal kinetic energies and their masses are 400 ~g . 1.2 ~kg and 1.6 ~kg respectively. The ratio of their linear momenta is :

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20

A player caught a cricket ball of mass 150 ~g moving at a speed of 20 ~m / s . If the catching process is completed in 0.1 ~s , the magnitude of force exerted by the ball on the

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21

A uniform thin metal plate of mass 10 ~kg with dimensions is shown. The ratio of x and y coordinates of center of mass of plate in (n)/(9) . The value of n is ________

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22

When kinetic energy of a body becomes 36 times of its original value, the percentage increase in the momentum of the body will be:

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23

Four particles A, B, C, D of mass (m)/(2), m, 2 m, 4 m , have same momentum, respectively. The particle with maximum kinetic energy is :

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24

In a system two particles of masses m_1=3 ~kg and m_2=2 ~kg are placed at certain distance from each other. The particle of mass m_1 is moved towards the center of mass of the

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25

A uniform rod AB of mass 2kg and Length 30cm at rest on a smooth horizontal surface. An impulse of force 0 . 2Ns is applied to end B. The time taken by the rod to turn through at

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26

The identical spheres each of mass 2M are placed at the corners of a right angled triangle with mutually perpendicular sides equal to 4m each. Taking point of intersection of

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27

A simple pendulum of length 1m has a wooden bob of mass 1kg . It is struck by a bullet of mass 10 ^ - 2 kg moving with a speed of 2 × 10 ^ 2 m s ^ - 1 . The bullet gets embedded

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28

A spherical body of mass 100g is dropped from a height of 10m from the ground. After hitting the ground, the body rebounds to a height of 5m . The impulse of force imparted by the

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29

A body of mass 1000kg is moving horizontally with a velocity 6m s ^ - 1 . If 200kg extra mass is added, the final velocity (in m s ^ - 1 ) is:

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30

A bar of mass M = 1 . 00kg and length L = 0 . 20m is lying on a horizontal frictionless surface. One end of the bar is pivoted at a point about which it is free to rotate. A small

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31

Two bodies are having kinetic energies in the ratio 16: 9 . If they have same linear momentum, the ratio of their masses respectively is:

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32

A bullet of 10g leaves the barrel of gun with a velocity of 600m s ^ - 1 . If the barrel of gun is 50cm long and mass of gun is 3kg, then value of impulse supplied to the gun will

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33

A nucleus disintegrates into two nuclear parts, in such a way that ratio of their nuclear sizes is 1: 2 ^ 1 / 3 . Their respective speed have a ratio of n: 1 . The value of n

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34

An average force of 125N is applied on a machine gun firing bullets each of mass 10g at the speed of 250m s ^ - 1 to keep it in position. The number of bullets fired per second by

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35

A particle of mass m moving with velocity v collides with a stationary particle of mass 2m . After collision, they stick together and continue to move together with velocity

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36

Figures (a), (b), (c) and (d) show variation of force with time. The impulse is highest in figure.

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37

A ball is dropped from a height of 20m . If the coefficient of restitution for the collision between ball and floor is 0 . 5 , after hitting the floor, the ball rebounds to a

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38

100 balls each of mass m moving with speed v simultaneously strike a wall normally and reflected back with same speed, in time ts . The total force exerted by the balls on the

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39

A machine gun of mass 10kg fires 20g bullets at the rate of 180 bullets per minute with a speed of 100m s ^ – 1 each. The recoil velocity of the gun is :

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40

As per the given figure, a small ball P slides down the quadrant of a circle and hits the other ball Q of equal mass which is initially at rest. Neglecting the effect of friction

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41

A ball of mass 200g rests on a vertical post of height 20m . A bullet of mass 10g , travelling in horizontal direction, hits the centre of the ball. After collision both travels

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42

A nucleus disintegrates into two smaller parts, which have their velocities in the ratio 3: 2 . The ratio of their nuclear sizes will be ((x)/(3))(1)/(3) . The value of ‘ x

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43

A body of mass 1kg collides head on elastically with a stationary body of mass 3kg . After collision, the smaller body reverses its direction of motion and moves with a speed of

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44

Two bodies of mass 1kg and 3kg have position vectors ^ i + 2 ^ j + ^ k and - 3 ^ i - 2 ^ j + ^ k respectively. The magnitude of position vector of centre of mass of this system

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45

The distance of centre of mass from end A of a one dimensional rod (AB) having mass density ρ = ρ _ 0 (1 - x ^ 2 L ^ 2 )kg m ^ - 1 and length L (in meter) is (3L)/(α)m . The value

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46

In two different experiments, an object of mass 5kg moving with a speed of 25 ms ^ - 1 hits two different walls and comes to rest within (i) 3 second, (ii) 5 seconds

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47

A ball of mass 0 . 15kg hits the wall with its initial speed of 12m s ^ - 1 and bounces back without changing its initial speed. If the force applied by the wall on the ball

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48

A body of mass 8kg and another of mass 2kg are moving with equal kinetic energy. The ratio of their respective momenta will be

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49

Two billiard balls of mass 0 . 05kg each moving in opposite directions with 10 ms ^ - 1 collide and rebound with the same speed. If the time duration of contact is t = 0 . 005s

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50

Three identical spheres each of mass M are placed at the corners of a right angled triangle with mutually perpendicular sides equal to 3m each. Taking point of intersection of

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51

A body of mass M at rest explodes into three pieces, in the ratio of masses 1: 1: 2 . Two smaller pieces fly off perpendicular to each other with velocities of 30 ms ^ - 1 and 40

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52

A man of 60kg is running on the road and suddenly jumps into a stationary trolly car of mass 120kg . Then the trolly car starts moving with velocity 2 ms ^ - 1 . The velocity of

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53

Two blocks of masses 10kg and 30kg are placed on the same straight line with coordinates (0, 0)cm and (x, 0)cm respectively. The block of 10kg is moved on the same line through a

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54

What percentage of kinetic energy of a moving particle is transferred to a stationary particle when it strikes the stationary particle of 5 times its mass? (Assume the collision

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55

A pendulum of length 2m consists of a wooden bob of mass 50g . A bullet of mass 75g is fired towards the stationary bob with a speed v . The bullet emerges out of the bob with a

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56

A batsman hits back a ball of mass 0 . 4kg straight in the direction of the bowler without changing its initial speed of 15 ms ^ - 1 . The impulse imparted to the ball is _____ Ns

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57

A body of mass M moving at speed V _ 0 collides elastically with a mass m at rest. After the collision, the two masses move at angles θ _ 1 and θ _ 2 with respect to the initial

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58

A bullet of 10g , moving with velocity v , collides head-on with the stationary bob of a pendulum and recoils with velocity 100m s ^ - 1 . The length of the pendulum is 0 . 5m and

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59

Three objects A, B and C are kept in a straight line on a frictionless horizontal surface. The masses of A, B and C are m, 2m and 2m respectively. A moves towards B with a speed

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60

A body of mass 2kg moving with a speed of 4m s ^ - 1 makes an elastic collision with another body at rest and continues to move in the original direction but with one fourth of

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61

The position of the centre of mass of a uniform semi-circular wire of radius R placed in x - y plane with its centre at the origin and the line joining its ends as x - axis is

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62

A body having specific charge 8μ C g ^ - 1 is resting on a frictionless plane at a distance 10cm from the wall (as shown in the figure). It starts moving towards the wall when a

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63

A rod of mass M and length L is lying on a horizontal frictionless surface. A particle of mass m travelling along the surface hits at one end of the rod with a velocity u in a

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64

An object of mass m _ 1 collides with another object of mass m _ 2 , which is at rest. After the collision the objects move with equal speeds in opposite direction. The ratio of

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65

A ball of mass 10kg moving with a velocity 10 3 m s ^ - 1 along the x -axis, hits another ball of mass 20kg which is at rest. After the collision, first ball comes to rest while

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66

A rubber ball is released from a height of 5m above the floor. It bounces back repeatedly, always rising to (81)/(100) of the height through which it falls. Find the average speed

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67

The disc of mass M with uniform surface mass density σ is shown in the figure. The center of mass of the quarter disc (the shaded area) is at the position ((xa)/(3π), (xa)/(3π))

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68

A large block of wood of mass M = 5 . 99kg is hanging from two long massless cords. A bullet of mass m = 10g is fired into the block and gets embedded in it. The (block + bullet)

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69

Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason R. Assertion A : Body P having mass M moving with speed u has head-on collision

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70

A circular hole of radius ((a)/(2)) is cut out of a circular disc of radius a as shown in figure. The centroid of the remaining circular portion with respect to point O will be:

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71

A ball with a speed of 9m s ^ - 1 collides with another identical ball at rest. After the collision, the direction of each ball makes an angle of 30 ° with the original direction.

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72

Particle A of mass m _ 1 moving with velocity ( 3 ^ i + ^ j ) ms ^ - 1 collides with another particle B of mass m _ 2 which is at rest initially. Let → v 1 and → v 2 be the

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73

The centre of mass of a solid hemisphere of radius 8cm is xcm from the centre of the flat surface. Then value of x is

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74

Two bodies of the same mass are moving with the same speed, but in different directions in a plane. They have a completely inelastic collision and move together thereafter with a

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75

A thin rod of mass 0 . 9kg and length 1m is suspended, at rest, from one end so that it can freely oscillate in the vertical plane. A particle of move 0 . 1kg moving in a straight

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76

A particle of mass 200MeV c ^ - 2 collides with a hydrogen atom at rest. Soon after the collision, the particle comes to rest, and the atom recoils and goes to its first excited

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77

Blocks of masses m, 2m, 4m and 8m are arranged in a line of a frictionless floor. Another block of mass m , moving with speed υ along the same line (see figure) collides with mass

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78

A block of mass 1 . 9kg is at rest at the edge of a table, of height 1 m. A bullet of mass 0 . 1kg collides with the block and sticks to it. If the velocity of the bullet is 20m s

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79

A square shaped hole of side l = (a)/(2) is carved out at a distance d = (a)/(2) from the centre ' O ' of a uniform circular disk of radius a. If the distance of the

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80

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

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81

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

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82

A rod of length l has non-uniform linear mass density given by ρ(x) = a + b ((x)/(l)) ^ 2 , where a and b are constants and 0 ≤ x ≤ l The value of x for the centre of mass of the

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83

A particle of mass m is projected with a speed u from the ground at an angle θ = (π)/(3) w.r.t. horizontal (x-axis). When it has reached its maximum height, it collides completely

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84

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:

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85

As shown in figure. When a spherical cavity (centred at O ) of radius 1 is cut out of a uniform sphere of radius R (centred at C ), the centre of mass of remaining (shaded part of

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86

A particle of mass m is dropped from a height h above the ground. At the same time another particle of the same mass is thrown vertically upwards from the ground with a speed of

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87

The coordinates of the centre of mass of a uniform flag-shaped lamina (thin flat plate) of mass 4kg . (The coordinates of the same are shown in the figure) are:

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88

Consider a uniform rod of mass M = 4m and length l pivoted about its centre. A mass m moving with velocity v making angle θ = (π)/(4) to the rod’s long axis collides with

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89

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 ^

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90

Three point particles of masses 1.0kg, 1.5kg and 2.5kg are placed at three corners of a right angle triangle of sides 4.0cm, 3.0cm and 5.0cm as shown in the figure. The centre of

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91

A ball of mass m moving with velocity v strikes the bob of a pendulum at rest. The mass of the bob is also m . If the collision is perfectly inelastic, the height to which the bob

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92

Two particles of equal mass have velocities → v 1 = 4 ^ i ^ -1 and → v 2 = 4 ^ j   ms ^ - 1 . First particle has an acceleration → a 1 = (5 ^ i

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93

A particle of mass 2 kg moving with a speed of 6 m/s collides elastically with another particle of mass 4 kg traveling in same direction with a speed of 2 m/s . The maximum

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94

A 500g ball is released from a height of 4m . Each time it makes contact with the ground, it loses 25% of its kinetic energy. Find the kinetic energy it possess just after the 3 ^

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95

A massive vertical wall is approaching a man at a speed u . When it is at a distance of 10m , the man throws a ball with speed 10m / s at an angle of 37 ° ,& which after having a

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96

A binary star consists of two stars A (mass= 22 M _ s ) and B (mass= 11 M _ s ), where M _ s is the mass of the sun. They are rotating about their centre of mass, which is

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97

A neutron collides elastically with the stationary nucleus of an atom of mass number A .& If the collision is perfectly elastic, then after the collision the fraction of the

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98

Two particles of equal mass& m are moving with velocities v ^ i and v ( ^ i + ^ j 2 )& respectively.& If the particles collide completely inelastically, then the energy lost in

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99

As shown in the figure a body of mass m moving vertically with speed 3m / s hits a smooth fixed inclined plane and rebounds with a velocity v _ f in the horizontal direction. If

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100

Two particles of masses m and 3m approach each other with different velocities. After collision, the particle of mass m has velocity → v in their centre of mass frame. Velocity of

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101

Three point masses 1. 0kg , 1. 5kg and 2. 5kg are placed at the vertices of a right-angle triangle of sides 4. 0cm , 3. 0cm and 5. 0cm ,& as shown in the figure. The centre of

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102

A particle of mass m is dropped from a height h above the ground. Simultaneously another particle of the same mass is thrown vertically upwards from the ground with a speed of 2gh

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103

A ball starts falling under the effect of gravitational force from a height of 45m . When it reaches a height of 25m it explodes into two pieces of mass ratio 1: 2 . There is no

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104

A radioactive nucleus at rest having& mass number A , emits an alpha-particle with speed v . The recoil speed of the daughter& nucleus is

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105

A block A of mass m is in equilibrium after being suspended from the ceiling with the help of a spring of force constant k . The block B of mass m , strikes the block A with a

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106

A projectile of mass 1 . 2kg undergoes a perfectly inelastic collision with a trolley of mass 3 . 6kg as shown in the figure. At the time of the collision, the speed of the

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107

Two blocks A and B of masses 3kg and 6kg are connected by a massless spring of force constant 1800N m ^ - 1 and then they are placed on a smooth horizontal surface. The blocks are

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108

An undeformed spring of spring constant k is connected to a bead of mass m which can move along a frictionless rod as shown in the figure. If the particle strikes the& bead at an

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109

A sphere of mass m moving with velocity v collides head-on with another sphere of the same mass at rest. If the coefficient of restitution e = (1)/(2) , then what is the ratio of

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110

There is a thin uniform disc of radius R and mass per unit area σ , in which a hole of radius R / 2 has been cut out as shown in the figure. Inside the hole, a square plate of

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111

A uniform solid right circular cone of base radius r is joined to a uniform solid hemisphere of radius r and of the same density, so as to have a common face. The centre of mass

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112

A small smooth disc of mass m and radius r moving with an initial velocity v along the positive x -axis collided with a big disc of mass 2m and radius 2r which was initially at

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113

A machine gun fires a bullet of mass 40g with a velocity 1200m s ^ - 1 . The man holding it can exert a maximum force of 144N on the gun. The maximum number of bullets that the

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114

Three objects A , B and C are kept in a straight line on a frictionless horizontal surface. These have masses m , 2m and m , respectively. The object A moves towards B with a

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115

A body of mass 3kg collides elastically with another body at rest and then continues to move in the original direction with one-half of its original speed. What is the mass of the

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116

A hemispherical cavity of radius R is created in a solid sphere of radius 2R as shown in the figure. The y -coordinate of the centre of mass of the remaining sphere is

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117

A spherical cavity is made in a lead sphere of radius R such that its surface touches the outside surface of lead sphere and passes through the centre. The shift in the centre of

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118

Three identical blocks A , B and C are placed on a horizontal frictionless surface. The blocks B and C are at rest but A is approaching towards B with a speed 10ms^ - 1 . The

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119

Two bodies of the same mass are connected with an inelastic string of length l are placed together on a horizontal surface. One of them is projected vertically upwards from the

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120

A ball is dropped from height H on to a horizontal surface. If the coefficient of restitution is e then the total time after which it comes to rest is

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