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Center of Mass, Momentum and Collision — JEE Main & Advanced Physics PYQs

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

358 questionsPhysicsSolutions on every page
1

Two identical bodies A and B of equal masses have initial velocities v₁ = 4 i m/s and v₂ = 4 j m/s respectively. The body A has acceleration a₁ = 6 i + 6 j m/s ^2 while the acceler

JEE Main 2026 Solution View → 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 _______.

JEE Main 2026 Solution View → 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 at

JEE Main 2026 Solution View → 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 linea

JEE Main 2026 Solution View → 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

JEE Main 2026 Solution View → 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 , respec

JEE Main 2026 Solution View → 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 : Th

JEE Main 2026 Solution View → 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 maximu

JEE Advanced 2025 Solution View → 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 )

JEE Main 2025 Solution View → 10

Consider two blocks A and B of masses m₁=10 ~kg and m₂=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 at

JEE Main 2025 Solution View → 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 dimension

JEE Main 2025 Solution View → 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 at rest

JEE Main 2025 Solution View → 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 mass

JEE Main 2025 Solution View → 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 accele

JEE Main 2025 Solution View → 15

The center of mass of a thin rectangular plate (fig - x ) with sides of length a and b , whose mass per unit area ( ) varies as = ₀ x a b (where ₀ is a constant), would be

JEE Main 2025 Solution View → 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 the

JEE Main 2025 Solution View → 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 p

JEE Advanced 2024 Solution View → 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, with

JEE Advanced 2024 Solution View → 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 :

JEE Main 2024 Solution View → 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 ha

JEE Main 2024 Solution View → 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 ________

JEE Main 2024 Solution View → 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:

JEE Main 2024 Solution View → 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 :

JEE Main 2024 Solution View → 24

In a system two particles of masses m₁=3 ~kg and m₂=2 ~kg are placed at certain distance from each other. The particle of mass m₁ is moved towards the center of mass of the system

JEE Main 2024 Solution View → 25

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

JEE Main 2024 Solution View → 26

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

JEE Main 2024 Solution View → 27

A simple pendulum of length 1 m has a wooden bob of mass 1 kg . 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 into t

JEE Main 2024 Solution View → 28

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

JEE Main 2024 Solution View → 29

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

JEE Main 2024 Solution View → 30

A bar of mass M = 1 . 00 kg and length L = 0 . 20 m 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 smal

JEE Advanced 2023 Solution View → 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:

JEE Main 2023 Solution View → 32

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

JEE Main 2023 Solution View → 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 is___

JEE Main 2023 Solution View → 34

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

JEE Main 2023 Solution View → 35

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

JEE Main 2023 Solution View → 36

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

JEE Main 2023 Solution View → 37

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

JEE Main 2023 Solution View → 38

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

JEE Main 2023 Solution View → 39

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

JEE Main 2023 Solution View → 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 a

JEE Main 2023 Solution View → 41

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

JEE Main 2023 Solution View → 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 ’ i

JEE Main 2023 Solution View → 43

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

JEE Main 2023 Solution View → 44

Two bodies of mass 1 kg and 3 kg 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 w

JEE Main 2022 Solution View → 45

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

JEE Main 2022 Solution View → 46

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

JEE Main 2022 Solution View → 47

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

JEE Main 2022 Solution View → 48

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

JEE Main 2022 Solution View → 49

Two billiard balls of mass 0 . 05 kg 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 . 005 s , t

JEE Main 2022 Solution View → 50

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

JEE Main 2022 Solution View → 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 m s - 1 and 40

JEE Main 2022 Solution View → 52

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

JEE Main 2022 Solution View → 53

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

JEE Main 2022 Solution View → 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 to

JEE Main 2022 Solution View → 55

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

JEE Main 2022 Solution View → 56

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

JEE Main 2022 Solution View → 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 initia

JEE Main 2021 Solution View → 58

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

JEE Main 2021 Solution View → 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 , 2 m and 2 m respectively. A moves towards B with a spe

JEE Main 2021 Solution View → 60

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

JEE Main 2021 Solution View → 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 give

JEE Main 2021 Solution View → 62

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

JEE Main 2021 Solution View → 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 dire

JEE Main 2021 Solution View → 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 the ma

JEE Main 2021 Solution View → 65

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

JEE Main 2021 Solution View → 66

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

JEE Main 2021 Solution View → 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 x a 3 π , x a 3

JEE Main 2021 Solution View → 68

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

JEE Main 2021 Solution View → 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 e

JEE Main 2021 Solution View → 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:

JEE Main 2021 Solution View → 71

A ball with a speed of 9 m 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 directi

JEE Main 2021 Solution View → 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

JEE Main 2020 Solution View → 73

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

JEE Main 2020 Solution View → 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 f

JEE Main 2020 Solution View → 75

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

JEE Main 2020 Solution View → 76

A particle of mass 200 MeV 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 sta

JEE Main 2020 Solution View → 77

Blocks of masses m , 2 m , 4 m and 8 m 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

JEE Main 2020 Solution View → 78

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

JEE Main 2020 Solution View → 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 centre of mass

JEE Main 2020 Solution View → 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 10 m at rest and then moves with half its initial kin

JEE Main 2020 Solution View → 81

A particle of mass m with an initial velocity u i ^ collides perfectly elastically with a mass 3 m at rest. It moves with a velocity v j ^ after collision, then, v is given by

JEE Main 2020 Solution View → 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

JEE Main 2020 Solution View → 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 compl

JEE Main 2020 Solution View → 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:

JEE Main 2020 Solution View → 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

JEE Main 2020 Solution View → 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 2

JEE Main 2020 Solution View → 87

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

JEE Main 2020 Solution View → 88

Consider a uniform rod of mass M = 4 m 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 w

JEE Main 2020 Solution View → 89

A body A of mass m = 0.1 k g 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

JEE Main 2020 Solution View → 90

Three point particles of masses 1.0 k g , 1.5 kg and 2.5 k g are placed at three corners of a right angle triangle of sides 4.0 c m , 3.0 c m and 5.0 c m as shown in the figure. Th

JEE Main 2020 Solution View → 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

NTA Abhyas JEE Main 2020 Solution View → 92

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

NTA Abhyas JEE Main 2020 Solution View → 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 possibl

NTA Abhyas JEE Main 2020 Solution View → 94

A 500 g ball is released from a height of 4 m . 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

NTA Abhyas JEE Main 2020 Solution View → 95

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

NTA Abhyas JEE Main 2020 Solution View → 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 stationary. Th

NTA Abhyas JEE Main 2020 Solution View → 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 initial

NTA Abhyas JEE Main 2020 Solution View → 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 the proces

NTA Abhyas JEE Main 2020 Solution View → 99

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

NTA Abhyas JEE Main 2020 Solution View → 100

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

NTA Abhyas JEE Main 2020 Solution View → 101

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

NTA Abhyas JEE Main 2020 Solution View → 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 2 g

NTA Abhyas JEE Main 2020 Solution View → 103

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

NTA Abhyas JEE Main 2020 Solution View → 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

NTA Abhyas JEE Main 2020 Solution View → 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 spee

NTA Abhyas JEE Main 2020 Solution View → 106

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

NTA Abhyas JEE Main 2020 Solution View → 107

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

NTA Abhyas JEE Main 2020 Solution View → 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 an

NTA Abhyas JEE Main 2020 Solution View → 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 final

NTA Abhyas JEE Main 2020 Solution View → 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 same

NTA Abhyas JEE Main 2020 Solution View → 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 of

NTA Abhyas JEE Main 2020 Solution View → 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 2 m and radius 2 r which was initially at r

NTA Abhyas JEE Main 2020 Solution View → 113

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

NTA Abhyas JEE Main 2020 Solution View → 114

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

NTA Abhyas JEE Main 2020 Solution View → 115

A body of mass 3 kg 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

NTA Abhyas JEE Main 2020 Solution View → 116

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

NTA Abhyas JEE Main 2020 Solution View → 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 m

NTA Abhyas JEE Main 2020 Solution View → 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 10 m s - 1 . The coef

NTA Abhyas JEE Main 2020 Solution View → 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 sur

NTA Abhyas JEE Main 2020 Solution View → 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

NTA Abhyas JEE Main 2020 Solution View →
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