Center of Mass and Collision PYQs - Last 10 Years

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Practice 114 JEE Main Physics questions from Center of Mass and Collision. Use the year-wise and type-wise breakdown to prioritize recent PYQs, then continue into the question list below.

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Last 10 Years Center of Mass and Collision Questions

Showing 50 of 114 filtered questions.

1Center Of Mass

Two masses of 3.4 kg and 2.5 kg are accelerated from an initial speed of $5 \mathrm{~m} / \mathrm{s}$ and $12 \mathrm{~m} / \mathrm{s}$, respectively. The distances traversed by the masses in the $5^{\text {th }}$ second are 104 m and 129 m...

INTEGER+4 / -12026

2Center Of Mass

The position of center of mass of three masses $2 \mathrm{~kg}, 3 \mathrm{~kg}$ and 15 kg placed with respect to mid point $(p)$ of normal bisector, as shown in the figure is $\_\_\_\_$ .

3Center Of Mass

Two identical bodies A and B of equal masses have initial velocities $\overrightarrow{v_1}=4 \hat{i} \mathrm{~m} / \mathrm{s}$ and $\overrightarrow{v_2}=4 \hat{j} \mathrm{~m} / \mathrm{s}$ respectively. The body A has acceleration $\overrig...

4Center Of Mass

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 rest at the same horizontal level and then released. The di...

5Center Of Mass

A small bob $A$ of mass $m$ is attached to a massless rigid rod of length 1 m pivoted at point $P$ and kept at an angle of $60^{\circ}$ with vertical as shown in figure. At distance of 1 m below point $P$, an identical bob $B$ is kept at re...

6Center Of Mass

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 $10 \mathrm{~m} / \mathrm{s}$ and $30 \mathrm{~m} / \mathrm{s}$, respectively, strike each ...

7Center Of Mass

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 with a speed of $18 \mathrm{~m} / \mathrm{s}$ each. The vel...

8Center Of Mass

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 : The total kinetic energy can be the sum of kinetic energy of t...

9Center Of Mass

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 $\mathrm{L}=10 \mathrm{~cm}$)

10Center Of Mass

Consider two blocks A and B of masses $m_1=10 \mathrm{~kg}$ and $\mathrm{m}_2=5 \mathrm{~kg}$ that are placed on a frictionless table. The block A moves with a constant speed $v=3 \mathrm{~m} / \mathrm{s}$ towards the block B kept at rest. ...

11Center Of Mass

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 on a frictionless table in the center. Assuming elastic collision, the mag...

12Center Of Mass

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 dimensional motion as shown in figure with initial velocities $v_{\ma...

13Center Of Mass

Three equal masses $m$ are kept at vertices $(A, B, C)$ of an equilateral triangle of side a in free space. At $t=0$, they are given an initial velocity $\overrightarrow{V_A}=V_0 \overrightarrow{A C}, \overrightarrow{V_B}=V_0 \overrightarr...

14Center Of Mass

The center of mass of a thin rectangular plate (fig - x ) with sides of length $a$ and $b$, whose mass per unit area $(\sigma)$ varies as $\sigma=\frac{\sigma_0 x}{a b}$ (where $\sigma_0$ is a constant), would be __________.

15Center Of Mass

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 edge of the disc. The distance of centre of mass of residua...

16Center Of Mass

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 plate in \(\frac{n}{9}\). The value of \(n\) is ________.

INTEGER+4 / -12024

17Center Of Mass

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 their kinetic energies \(\left(K_B: K_A\right)\) is :

18Center Of Mass

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 mass \(m_1\) is moved towards the center of mass of the system through a distance $$2 \mat...

INTEGER+4 / -12024

19Center Of Mass

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 direction of the velocity of the body becomes horizontal. The value of \(\frac{H}{h}\) for ...

INTEGER+4 / -12024

20Center Of Mass

A solid circular disc of mass \(50 \mathrm{~kg}\) rolls along a horizontal floor so that its center of mass has a speed of \(0.4 \mathrm{~m} / \mathrm{s}\). The absolute value of work done on the disc to stop it is ________ J.

INTEGER+4 / -12024

21Center Of Mass

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 artillery and that of the shell is:

22Center Of Mass

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 rebounds to a height of \(5 \mathrm{~m}\). The impulse of force imparted by the ground to the bo...

23Center Of Mass

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 added, the final velocity (in \(\mathrm{m} / \mathrm{s}\)) is:

24Center Of Mass

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 :

25Center Of Mass

Three identical spheres each of mass $2 \mathrm{M}$ are placed at the corners of a right angled triangle with mutually perpendicular sides equal to $4 \mathrm{~m}$ each. Taking point of intersection of these two sides as origin, the magnitu...

INTEGER+4 / -12024

26Center Of Mass

The momentum of a body is increased by \(50 \%\). The percentage increase in the kinetic energy of the body is ___________ \(\%\).

INTEGER+4 / -12023

27Center Of Mass

100 balls each of mass \(\mathrm{m}\) moving with speed \(v\) simultaneously strike a wall normally and reflected back with same speed, in time \(\mathrm{t ~s}\). The total force exerted by the balls on the wall is

28Center Of Mass

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 hitting the floor, the ball rebounds to a height of ________ $\mathrm{m}$.

INTEGER+4 / -12023

29Center Of Mass

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 horizontal direction, hits the centre of the ball. After collision both travels independently. The ...

30Center Of Mass

The figure represents the momentum time (\(\mathrm{p}-\mathrm{t}\)) curve for a particle moving along an axis under the influence of the force. Identify the regions on the graph where the magnitude of the force is maximum and minimum respec...

31Center Of Mass

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 and assume the collision to be elastic, the velocity of ball ...

32Center Of Mass

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 $100 \mathrm{~m} \mathrm{~s}^{-1}$ each. The recoil velocity of the gun is

33Center Of Mass

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 2 m/s. The initial speed of the smaller body before collision...

INTEGER+4 / -12023

34Center Of Mass

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 \(50 \mathrm{~cm}\) long and mass of gun is \(3 \mathrm{~kg}\), then value of impulse supplied to the gun w...

35Center Of Mass

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 \(250 \mathrm{~m} / \mathrm{s}\) to keep it in position. The number of bullets fired per second by the machin...

36Center Of Mass

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

37Center Of Mass

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 energies will be :

38Center Of Mass

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 ms\(-\)1 respectively. The velocity of the third piece will ...

39Center Of Mass

Two bodies of mass \(1 \mathrm{~kg}\) and \(3 \mathrm{~kg}\) have position vectors \(\hat{i}+2 \hat{j}+\hat{k}\) and \(-3 \hat{i}-2 \hat{j}+\hat{k}\) respectively. The magnitude of position vector of centre of mass of this system will be si...

40Center Of Mass

If momentum of a body is increased by 20%, then its kinetic energy increases by

41Center Of Mass

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 ms\(-\)1. The velocity of the running man was ___________ ms\(-\)1, when he jumps into ...

INTEGER+4 / -12022

42Center Of Mass

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 to rest within (i) 3 second, (ii) 5 seconds, respectively. Choose the correct option out o...

43Center Of Mass

The distance of centre of mass from end A of a one dimensional rod (AB) having mass density \(\rho=\rho_{0}\left(1-\frac{x^{2}}{L^{2}}\right) \mathrm{kg} / \mathrm{m}\) and length L (in meter) is \(\frac{3 L}{\alpha} \mathrm{m}\). The value...

INTEGER+4 / -12022

44Center Of Mass

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 be head-on elastic collision)

45Center Of Mass

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 a distance of 6 cm towards the other block. The distance t...

46Center Of Mass

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 through a point \((20,10)\). If \(\mathrm{T}\) is the time of flight, then its momentum vector...

47Center Of Mass

An object is thrown vertically upwards. At its maximum height, which of the following quantity becomes zero?

48Center Of Mass

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 imparted to the ball is ___________ Ns.

INTEGER+4 / -12022

49Center Of Mass

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 will be :

50Center Of Mass

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 speed. If the force applied by the wall on the ball during the contact is $$100 \mathrm{~N}$...