# Center of Mass and Collision · Physics · JEE Main

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JEE Main 2024 (Online) 8th April Morning Shift
A stationary particle breaks into two parts of masses $$m_A$$ and $$m_B$$ which move with velocities $$v_A$$ and $$v_B$$ respectively. The ratio of th...
JEE Main 2024 (Online) 31st January Morning Shift
An artillery piece of mass $$M_1$$ fires a shell of mass $$M_2$$ horizontally. Instantaneously after the firing, the ratio of kinetic energy of the ar...
JEE Main 2024 (Online) 30th January Morning Shift
A spherical body of mass $$100 \mathrm{~g}$$ is dropped from a height of $$10 \mathrm{~m}$$ from the ground. After hitting the ground, the body reboun...
JEE Main 2024 (Online) 27th January Morning Shift
Two bodies of mass $$4 \mathrm{~g}$$ and $$25 \mathrm{~g}$$ are moving with equal kinetic energies. The ratio of magnitude of their linear momentum is...
JEE Main 2024 (Online) 27th January Morning Shift
A body of mass $$1000 \mathrm{~kg}$$ is moving horizontally with a velocity $$6 \mathrm{~m} / \mathrm{s}$$. If $$200 \mathrm{~kg}$$ extra mass is adde...
JEE Main 2023 (Online) 13th April Morning Shift
A bullet of $$10 \mathrm{~g}$$ leaves the barrel of gun with a velocity of $$600 \mathrm{~m} / \mathrm{s}$$. If the barrel of gun is $$50 \mathrm{~cm}... JEE Main 2023 (Online) 11th April Morning Shift An average force of$$125 \mathrm{~N}$$is applied on a machine gun firing bullets each of mass$$10 \mathrm{~g}$$at the speed of$$250 \mathrm{~m} /...
JEE Main 2023 (Online) 10th April Morning Shift
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 ...
JEE Main 2023 (Online) 31st January Morning Shift
100 balls each of mass $$\mathrm{m}$$ moving with speed $$v$$ simultaneously strike a wall normally and reflected back with same speed, in time $$\mat... JEE Main 2023 (Online) 30th January Evening Shift A machine gun of mass 10 \mathrm{~kg} fires 20 \mathrm{~g} bullets at the rate of 180 bullets per minute with a speed of 100 \mathrm{~m} \mathrm{... JEE Main 2023 (Online) 30th January Morning Shift As per the given figure, a small ball P slides down the quadrant of a circle and hits the other ball Q of equal mass which is initially at rest. Negle... JEE Main 2023 (Online) 30th January Morning Shift The figure represents the momentum time ($$\mathrm{p}-\mathrm{t}$$) curve for a particle moving along an axis under the influence of the force. Identi... JEE Main 2023 (Online) 30th January Morning Shift A ball of mass$$200 \mathrm{~g}$$rests on a vertical post of height$$20 \mathrm{~m}$$. A bullet of mass$$10 \mathrm{~g}$$, travelling in horizonta... JEE Main 2022 (Online) 29th July Evening Shift If momentum of a body is increased by 20%, then its kinetic energy increases by JEE Main 2022 (Online) 29th July Morning Shift Two bodies of mass$$1 \mathrm{~kg}$$and$$3 \mathrm{~kg}$$have position vectors$$\hat{i}+2 \hat{j}+\hat{k}$$and$$-3 \hat{i}-2 \hat{j}+\hat{k}$$... JEE Main 2022 (Online) 28th July Morning Shift In two different experiments, an object of mass$$5 \mathrm{~kg}$$moving with a speed of$$25 \mathrm{~ms}^{-1}$$hits two different walls and comes ... JEE Main 2022 (Online) 27th July Evening Shift A body of mass$$10 \mathrm{~kg}$$is projected at an angle of$$45^{\circ}$$with the horizontal. The trajectory of the body is observed to pass thro... JEE Main 2022 (Online) 26th July Evening Shift A ball of mass$$0.15 \mathrm{~kg}$$hits the wall with its initial speed of$$12 \mathrm{~ms}^{-1}$$and bounces back without changing its initial sp... JEE Main 2022 (Online) 26th July Evening Shift A body of mass$$8 \mathrm{~kg}$$and another of mass$$2 \mathrm{~kg}$$are moving with equal kinetic energy. The ratio of their respective momentum ... JEE Main 2022 (Online) 25th July Evening Shift Two billiard balls of mass 0.05 kg each moving in opposite directions with 10 ms$$-$$1 collide and rebound with the same speed. If the time duration o... JEE Main 2022 (Online) 30th June Morning Shift Two bodies A and B of masses 5 kg and 8 kg are moving such that the momentum of body B is twice that of the body A. The ratio of their kinetic energie... JEE Main 2022 (Online) 29th June Morning Shift A body of mass M at rest explodes into three pieces, in the ratio of masses 1 : 1 : 2. Two smaller pieces fly off perpendicular to each other with vel... JEE Main 2022 (Online) 27th June Morning Shift Two blocks of masses 10 kg and 30 kg are placed on the same straight line with coordinates (0, 0) cm and (x, 0) cm respectively. The block of 10 kg is... JEE Main 2022 (Online) 27th June Morning Shift What percentage of kinetic energy of a moving particle is transferred to a stationary particle when it strikes the stationary particle of 5 times its ... JEE Main 2022 (Online) 26th June Morning Shift An object is thrown vertically upwards. At its maximum height, which of the following quantity becomes zero? JEE Main 2021 (Online) 31st August Morning Shift A body of mass M moving at speed V0 collides elastically with a mass 'm' at rest. After the collision, the two masses move at angles$$\theta$$1 and ... JEE Main 2021 (Online) 27th July Morning Shift Three objects A, B and C are kept in a straight line on a frictionless horizontal surface. The masses of A, B and C are m, 2m and 2m respectively. A m... JEE Main 2021 (Online) 25th July Morning Shift Two billiard balls of equal mass 30g strike a rigid wall with same speed of 108 kmph (as shown) but at different angles. If the balls get reflected wi... JEE Main 2021 (Online) 22th July Evening Shift A bullet of '4 g' mass is fired from a gun of mass 4 kg. If the bullet moves with the muzzle speed of 50 ms$$-$$1, the impulse imparted to the gun and... JEE Main 2021 (Online) 20th July Evening Shift If the Kinetic energy of a moving body becomes four times its initial Kinetic energy, then the percentage change in its momentum will be : JEE Main 2021 (Online) 18th March Evening Shift An object of mass m1 collides with another object of mass m2, which is at rest. After the collision the objects move with equal speeds in opposite dir... JEE Main 2021 (Online) 17th March Evening Shift Two identical blocks A and B each of mass m resting on the smooth horizontal floor are connected by a light spring of natural length L and spring cons... JEE Main 2021 (Online) 16th March Evening Shift A large block of wood of mass M = 5.99 kg is hanging from two long massless cords. A bullet of mass m = 10 g is fired into the block and gets embedded... JEE Main 2021 (Online) 16th March Morning Shift Four equal masses, m each are placed at the comers of a square of length (l) as shown in the figure. The moment of inertia of the system about an axis... JEE Main 2021 (Online) 26th February Morning Shift Given below are two statements : one is labelled as Assertion A and the other is labelled as Reason R.Assertion A : Body 'P' having mass M moving with... JEE Main 2021 (Online) 24th February Evening Shift A circular hole of radius$$\left( {{a \over 2}} \right)$$is cut out of a circular disc of radius 'a' as shown in figure. The centroid of the remaini... JEE Main 2020 (Online) 6th September Evening Slot Particle A of mass m1 moving with velocity$$\left( {\sqrt3\widehat i + \widehat j} \right)m{s^{ - 1}}$$collides with another particle B of mass m2 ... JEE Main 2020 (Online) 4th September Morning Slot Blocks of masses m, 2m, 4m and 8m are arranged in a line on a frictionless floor. Another block of mass m, moving with speed v along the same line (se... JEE Main 2020 (Online) 3rd September Evening Slot A block of mass 1.9 kg is at rest at the edge of a table, of height 1 m. A bullet of mass 0.1 kg collides with the block and sticks to it. If the velo... JEE Main 2020 (Online) 3rd September Morning Slot A block of mass m = 1 kg slides with velocity v = 6 m/s on a frictionless horizontal surface and collides with a uniform vertical rod and sticks to it... JEE Main 2020 (Online) 2nd September Morning Slot A particle of mass m with an initial velocity$$u\widehat i$$collides perfectly elastically with a mass 3 m at rest. It moves with a velocity$$v\wid...
JEE Main 2020 (Online) 9th January Evening Slot
A rod of length L has non-uniform linear mass density given by $$\rho$$(x) = $$a + b{\left( {{x \over L}} \right)^2}$$ , where a and b are constants ...
JEE Main 2020 (Online) 9th January Evening Slot
A particle of mass m is projected with a speed u from the ground at an angle $$\theta = {\pi \over 3}$$ w.r.t. horizontal (x-axis). When it has reac...
JEE Main 2020 (Online) 9th January Morning Slot
Two particles of equal mass m have respective initial velocities $$u\widehat i$$ and $$u\left( {{{\widehat i + \widehat j} \over 2}} \right)$$. They c...
JEE Main 2020 (Online) 8th January Evening Slot
As shown in figure, when a spherical cavity (centered at O) of radius 1 is cut out of a uniform sphere of radius R (centered at C), the centre of mass...
JEE Main 2020 (Online) 8th January Evening Slot
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...
JEE Main 2020 (Online) 8th January Morning Slot
The coordinates of centre of mass of a uniform flag shaped lamina (thin flat plate) of mass 4kg. (The coordinates of the same are shown in figure) are...
JEE Main 2020 (Online) 7th January Morning Slot
Three point particles of masses 1.0 kg, 1.5 kg and 2.5 kg are placed at three corners of a right angle triangle of sides 4.0 cm, 3.0 cm and 5.0 cm as ...
JEE Main 2019 (Online) 12th April Evening Slot
Three particles of masses 50 g, 100 g and 150 g are placed at the vertices of an equilateral triangle of side 1 m (as shown in the figure). The (x, y)...
JEE Main 2019 (Online) 12th April Morning Slot
A man (mass = 50 kg) and his son (mass = 20 kg) are standing on a frictionless surface facing each other. The man pushes his son so that he starts mov...
JEE Main 2019 (Online) 10th April Morning Slot
Two particles, of masses M and 2M, moving, as shown, with speeds of 10 m/s and 5 m/s, collide elastically at the origin. After the collision, they mov...
JEE Main 2019 (Online) 9th April Evening Slot
A particle of mass 'm' is moving with speed '2v' and collides with a mass '2m' moving with speed 'v' in the same direction. After collision, the first...
JEE Main 2019 (Online) 9th April Evening Slot
A wedge of mass M = 4m lies on a frictionless plane. A particle of mass m approaches the wedge with speed v. There is no friction between the particle...
JEE Main 2019 (Online) 9th April Morning Slot
A body of mass 2 kg makes an eleastic collision with a second body at rest and continues to move in the original direction but with one fourth of its ...
JEE Main 2019 (Online) 9th April Morning Slot
A ball is thrown vertically up (taken as +z-axis) from the ground. The correct momentum-height (p-h) diagram is :
JEE Main 2019 (Online) 8th April Evening Slot
A uniform rectangular thin sheet ABCD of mass M has length a and breadth b, as shown in the figure. If the shaded portion HBGO is cut-off, the coordin...
JEE Main 2019 (Online) 8th April Evening Slot
A body of mass m1 moving with an unknown velocity of $${v_1}\mathop i\limits^ \wedge$$, undergoes a collinear collision with a body of mass m2 movin...
JEE Main 2019 (Online) 8th April Morning Slot
Four particles A, B, C and D with masses mA = m, mB = 2m, mC = 3m and mD = 4m are at the corners of a square. They have accelerations of equal magnitu...
JEE Main 2019 (Online) 8th April Morning Slot
If 1022 gas molecules each of mass 10–26 kg collide with a surface (perpendicular to it) elastically per second over an area 1 m2 with a speed 104 m/s...
JEE Main 2019 (Online) 12th January Evening Slot
An alpha-particle of mass m suffers 1-dimensional elastic collision with a nucleus at rest of unknown mass. It is scattered directly backwards losing,...
JEE Main 2019 (Online) 12th January Morning Slot
The position vector of the centre of mass $$\overrightarrow r {\,_{cm}}\,$$ of an asymmetric uniform bar of negligible area of crosssection as shown i...
JEE Main 2019 (Online) 12th January Morning Slot
A simple pendulum, made of a string of length $$\ell$$ and a bob of mass m, is released from a small angle $${{\theta _0}}$$. It strikes a block of m...
JEE Main 2019 (Online) 11th January Evening Slot
A particle of mass m is moving in a straight line with momentum p. Starting at time t = 0, a force F = kt acts in the same direction on the moving par...
JEE Main 2019 (Online) 11th January Morning Slot
A body of mass 1 kg falls freely from a height of 100 m, on a platform mass 3 kg which is mounted on a spring having spring constant k = 1.25 $$\time... JEE Main 2019 (Online) 10th January Morning Slot A piece of wood of mass 0.03 kg is dropped from the top of a 100 m height building. At the same time, a bullet of mass 0.02 kg is fired vertically upw... JEE Main 2019 (Online) 9th January Morning Slot Two masses m and$${m \over 2}$$are connected at the two ends of a massless rigid rod of length l. The rod is suspended by a thin wire of torsional c... JEE Main 2019 (Online) 9th January Morning Slot Three blocks A, B and C are lying on a smooth horizontal surface, as shown in the figure. A and B have equal masses, m while C has mass M, Block A is ... JEE Main 2018 (Offline) In a collinear collision, a particle with an initial speed v0 strikes a stationary particle of the same mass. If the final total kinetic energy is 50%... JEE Main 2018 (Offline) The mass of a hydrogen molecule is 3.32$$\times$$10-27 kg. If 1023 hydrogen molecules strike, per second, a fixed wall of area 2 cm2 at an angle of ... JEE Main 2018 (Online) 15th April Evening Slot A proton of mass m collides elastically with a particle of unknown mass at rest. After the collision, the proton and the unknown particle are seen mo... JEE Main 2017 (Online) 9th April Morning Slot Two particles A and B of equal mass M are moving with the same speed$$\upsilon $$as shown in the figure. They collide completely inelastically and m... JEE Main 2016 (Online) 10th April Morning Slot A neutron moving with a speed ‘v’ makes a head on collision with a stationary hydrogen atom in ground state. The minimum kinetic energy of the neutron... JEE Main 2016 (Online) 10th April Morning Slot In the figure shown ABC is a uniform wire. If centre of mass of wire lies vertically below point A, then$${{BC} \over {AB}}$$is close to : ... JEE Main 2015 (Offline) A particle of mass$$m$$moving in the$$x$$direction with speed$$2v$$is hit by another particle of mass$$2m$$moving in the$$y$$direction with... JEE Main 2015 (Offline) Distance of the center of mass of a solid uniform cone from its vertex is$$z{}_0$$. If the radius of its base is$$R$$and its height is$$h$$then ... JEE Main 2013 (Offline) This question has statement$${\rm I}$$and statement$${\rm I}{\rm I}$$. Of the four choices given after the statements, choose the one that best... AIEEE 2010 Statement - 1 : Two particles moving in the same direction do not lose all their energy in a completely inelastic collision. Statement - 2 : Princip... AIEEE 2010 The figure shows the position$$-$$time$$(x-t)$$graph of one-dimensional motion of body of mass$$0.4kg.$$The magnitude of each impulse is ... AIEEE 2008 A block of mass$$0.50kg$$is moving with a speed of$$2.00m{s^{ - 1}}$$on a smooth surface. It strike another mass of$$1.0kg$$and t... AIEEE 2008 A thin rod of length$$'L'$$is lying along the$$x$$-axis with its ends at$$x=0$$and$$x=L$$. Its linear density (mass/length) varies with$$x$$as... AIEEE 2007 A circular disc of radius$$R$$is removed from a bigger circular disc of radius$$2R$$such that the circumferences of the discs coincide. The center... AIEEE 2006 A player caught a cricket ball of mass$$150g$$moving at a rate of$$20m/s.$$If the catching process is completed in$$0.1s,$$the force ... AIEEE 2006 A bomb of mass$$16kg$$at rest explodes into two pieces of masses$$4kg$$and$$12kg.$$The velocity of the$$12kg$$mass is$$4\,\,m{...
AIEEE 2006
Consider a two particle system with particles having masses $${m_1}$$ and $${m_2}$$. If the first particle is pushed towards the center of mass throug...
AIEEE 2005
A body $$A$$ of mass $$M$$ while falling vertically downloads under gravity breaks into two-parts; a body $$B$$ of mass $${1 \over 3}$$ $$M$$ and a bo...
AIEEE 2005
The block of mass $$M$$ moving on the frictionless horizontal surface collides with the spring of spring constant $$k$$ and compresses it by length $$... AIEEE 2005 A mass$$'m'$$moves with a velocity$$'v'$$and collides inelastically with another identical mass. After collision the$${1^{st}}$$mass moves with ... AIEEE 2005 A T shaped object with dimensions shown in the figure, is lying on a smooth floor. A force$$'\,\,\overrightarrow F \,\,'$$is applied at the point$$...
AIEEE 2004
A machine gun fires a bullet of mass $$40$$ $$g$$ with a velocity $$1200m{s^{ - 1}}.$$ The man holding it can exert a maximum force of $$144$$ $$N$$ ...
AIEEE 2003
Consider the following two statements : $$A.$$ Linear momentum of a system of particles is zero $$B.$$ Kinetic energy of a system of particles is zer...
AIEEE 2002
Two identical particles move towards each other with velocity $$2v$$ and $$v$$ respectively. The velocity of center of mass is

## Numerical

JEE Main 2024 (Online) 8th April Morning Shift
A uniform thin metal plate of mass $$10 \mathrm{~kg}$$ with dimensions is shown. The ratio of $$\mathrm{x}$$ and y coordinates of center of mass of pl...
JEE Main 2024 (Online) 4th April Evening Shift
In a system two particles of masses $$m_1=3 \mathrm{~kg}$$ and $$m_2=2 \mathrm{~kg}$$ are placed at certain distance from each other. The particle of ...
JEE Main 2024 (Online) 1st February Morning Shift
The identical spheres each of mass $2 \mathrm{M}$ are placed at the corners of a right angled triangle with mutually perpendicular sides equal to $4 \... JEE Main 2024 (Online) 31st January Morning Shift A solid circular disc of mass $$50 \mathrm{~kg}$$ rolls along a horizontal floor so that its center of mass has a speed of $$0.4 \mathrm{~m} / \mathrm... JEE Main 2024 (Online) 31st January Morning Shift A body starts falling freely from height$$H$$hits an inclined plane in its path at height$$h$$. As a result of this perfectly elastic impact, the d... JEE Main 2023 (Online) 8th April Morning Shift The momentum of a body is increased by$$50 \%$$. The percentage increase in the kinetic energy of the body is ___________$$\%$$. JEE Main 2023 (Online) 31st January Evening Shift A ball is dropped from a height of 20 \mathrm{~m}. If the coefficient of restitution for the collision between ball and floor is 0.5, after hittin... JEE Main 2023 (Online) 25th January Evening Shift A body of mass 1 kg collides head on elastically with a stationary body of mass 3 kg. After collision, the smaller body reverses its direction of moti... JEE Main 2022 (Online) 28th July Evening Shift The distance of centre of mass from end A of a one dimensional rod (AB) having mass density$$\rho=\rho_{0}\left(1-\frac{x^{2}}{L^{2}}\right) \mathrm{... JEE Main 2022 (Online) 25th July Evening Shift 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. Takin... JEE Main 2022 (Online) 28th June Morning Shift 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... JEE Main 2022 (Online) 26th June Evening Shift 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 ms$$-$$1. The impulse impar... JEE Main 2021 (Online) 27th August Evening Shift 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. The length of the ... JEE Main 2021 (Online) 25th July Morning Shift A body of mass 2 kg moving with a speed of 4 m/s. makes an elastic collision with another body at rest and continues to move in the original direction... JEE Main 2021 (Online) 22th July Evening Shift 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 joinin... JEE Main 2021 (Online) 20th July Morning Shift 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... JEE Main 2021 (Online) 18th March Evening Shift The projectile motion of a particle of mass 5 g is shown in the figure.The initial velocity of the particle is $$5\sqrt 2$$ ms-1 and the air resistan... JEE Main 2021 (Online) 18th March Morning Shift A ball of mass 10 kg moving with a velocity 10$$\sqrt 3$$ m/s along the x-axis, hits another ball of mass 20 kg which is at rest. After the collision... JEE Main 2021 (Online) 17th March Evening Shift The disc of mass M with uniform surface mass density $$\sigma$$ is shown in the figure. The centre of mass of the quarter disc (the shaded area) is at... JEE Main 2021 (Online) 16th March Morning Shift A ball of mass 10 kg moving with a velocity $$10\sqrt 3$$ m s$$-$$1 along X-axis, hits another ball of mass 20 kg which is at rest. After collision, ... JEE Main 2021 (Online) 25th February Evening Shift Two particles having masses 4 g and 16 g respectively are moving with equal kinetic energies. The ratio of the magnitudes of their linear momentum is ... JEE Main 2021 (Online) 24th February Evening Shift Two solids A and B of mass 1 kg and 2 kg respectively are moving with equal linear momentum. The ratio of their kinetic energies (K.E.)A : (K.E.)B wil... JEE Main 2021 (Online) 24th February Morning Shift A ball with a speed of 9 m/s collides with another identical ball at rest. After the collision, the direction of each ball makes an angle of 30$$^\cir... JEE Main 2020 (Online) 6th September Evening Slot The centre of mass of solid hemisphere of radius 8 cm is x from the centre of the flat surface. Then value of x is __________. JEE Main 2020 (Online) 6th September Morning Slot Two bodies of the same mass are moving with the same speed, but in different directions in a plane. They have a completely inelastic collision and mov... JEE Main 2020 (Online) 2nd September Evening Slot A particle of mass m is moving along the x-axis with initial velocity$$u\widehat i$$. It collides elastically with a particle of mass 10 m at rest an... JEE Main 2020 (Online) 2nd September Evening Slot A square shaped hole of side l =$${a \over 2}$$is carved out at a distance d =$${a \over 2}$$from the centre ‘O’ of a uniform circular disk of rad... JEE Main 2020 (Online) 8th January Morning Slot A body A, of mass m = 0.1 kg has an initial velocity of 3$$\widehat i$\$ ms-1 . It collides elastically with another body, B of the same mass which has...
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