Conservation of Momentum — JEE Main PYQs

A uniform bar of length 12 cm and mass $20m$ lies on a smooth horizontal table. Two point masses m and $2m$ are moving in opposite directions with same speed of v and in the same plane as the bar, as shown in figure. These masses strike the bar simultaneously and get stuck to it. …

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 the center of mass w.r.t. to the origin and …

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 rest on a smooth horizontal surface that extends t …

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 other and stick together. The rise in tem …

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 velocity of the heavier fragment is _\ …

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 distance traversed by the centre of mass i …

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 ______.

Two identical bodies A and B of equal masses have initial velocities ${\overrightarrow{v}}_1=4\hat{i}$ m/s and ${\overrightarrow{v}}_2=4\hat{j}$ m/s respectively. The body A has acceleration ${\overrightarrow{a}}_1=6\hat{i}+6\hat{j}$ m/s${}^2$ while the acceleration of th …

Consider a circular disc of radius 20 cm with centre located at the origin. A circular hole of a 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 residual or remaining disc from the origin wi …

Given below are two statements. One is labelled as Assertion (A) and the other is labelled as Reason (R).

Three identical spheres of same mass undergo one dimensional motion as shown in figure with initial velocities …

Three equal masses $m$ are kept at vertices ( $A,B,C$ ) of an equilateral triangle of side a in free space. At $\mathrm{t}=0$, they are given an initial velocity ${\vec{V}}_A=V_0\overrightarrow{AC},{\vec{V}}_B=V_0\overrightarrow{BA}$ and …

As shown below, bob A of a pendulum having massless string of length ' R ' is released from $60^{\circ }$ to the vertical. It hits another bob B of half the mass that is at rest on a friction less table in the centre. Assuming elastic collision, the magnitude of the velocity of bo …

The centre of mass of a thin rectangular plate (fig x ) with sides of length a and b , whose mass per unit area $(\sigma )$ varies as $\sigma =\frac{{\sigma }_0\mathrm{X}}{\mathrm{ab}}$ (where ${\sigma }_0$ is a constant), would be $\_\_\_\_$

Consider two blocks A and B of masses ${\mathrm{m}}_1=10\mathrm{kg}$ 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. A spring with spring …

A small mirror of mass m is suspended by a massless thread of length $l$. Then the small angle through which the thread will be deflected when a short pulse of laser of energy E falls normal on the mirror
( $\mathrm{c}=$ speed of light in vacuum and $\mathrm{g}=$ acceleration due …

A rod of length 5L is bent right angle keeping one side length as 2L.

The position of the centre of mass of the system: (Consider L = 10 cm)

In a system two particles of masses $m_1=3\text{kg}$ and $m_2=2\text{kg}$ 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 cm . In order to keep the center of mass …

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

A stationary particle breaks into two parts of masses ${\mathrm{m}}_{\mathrm{A}}$ and ${\mathrm{m}}_{\mathrm{B}}$ which move with velocities ${\mathrm{v}}_{\mathrm{A}}$ and ${\mathrm{v}}_{\mathrm{B}}$ respectively. The ratio of their kinetic energies ( …

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 $\frac{n}{9}$.The value of n is ____.

A nucleus at rest disintegrates into two smaller nuclei with their masses in the ratio of $2:1$. After disintegration they will move :-

Two bodies of mass 4 g and 25 g are moving with equal kinetic energies. The ratio of magnitude of their linear momentum is :

A body of mass 1000 kg is moving horizontally with a velocity $6\mathrm{m}/\mathrm{s}$. If 200 kg extra mass is added, the final velocity (in $\mathrm{m}/\mathrm{s}$) is:

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:

A cricket player catches a ball of mass 120 g moving with $25\mathrm{m}/\mathrm{s}$ speed. If the catching process is completed in 0.1 s then the magnitude of force exerted by the ball on the hand of player will be (in SI unit):

A simple pendulum of length 1 m has a wooden bob of mass 1 kg . It is struck by a bullet of mass $10^{-2}\mathrm{kg}$ moving with a speed of $2\times 10^2{\mathrm{ms}}^{-1}$. The bullet gets embedded into the bob. The height to which the bob rises before swinging back is. …

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 these two sides as origin, the magnitude of position vector of the centre of mass of the system is …

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 the ground to the body is given by : (given $\mathrm{g}=9.8\mathrm{m}/{\mathrm{s}}^2$ )

A bullet of mass 0.1 kg moving horizontally with speed $400{\mathrm{ms}}^{-1}$ hits a wooden block of mass 3.9 kg kept on a horizontal rough surface. The bullet gets embedded into the block and moves 20 m before coming to rest. The coefficient of friction between the block and th …

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

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

A bullet 10 g leaves the barrel of gun with a velocity of $600\mathrm{m}/\mathrm{s}$. If the barrel of gun is 50 cm long and mass of gun is 3 kg , then value of impulse supplied to the gun will be :

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

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 $\_\_\_\_$

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 $2m/s$. The initial speed of the smaller body before collision is ____ ${\mathrm{ms}}^{-1}$.

A tennis ball is dropped on to the floor from a height of 9.8 m. It rebounds to a height 5.0 m. Ball comes in contact with the floor for 0.2 s. The average acceleration during contact is ______ $\mathrm{m}{\mathrm{s}}^{-2}$. [Given $g=10\mathrm{m}{\mathrm{s}}^{-2}$]

A machine gun of mass 10 kg fires 20 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 :

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 Q after collision will be : …

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 independently. The ball hits the ground at a distance 30 m and the bullet at a distance of 120 m from …

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 wall is

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 height of ______ m.

Figures (a), (b), (c) and (d) show variation of force with time.

The impulse is highest in figure.

In two different experiments, an object of mass 5 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 of the following :

A balloon has mass of 10 g in air. The air escapes from the balloon at a uniform rate with velocity $4.5\mathrm{cm}/\mathrm{s}$. If the balloon shrinks in 5 s completely. Then, the average force acting on that balloon will be (in dyne).

A pressure-pump has a horizontal tube of cross-sectional area $10{\mathrm{cm}}^2$ for the outflow of water at a speed of $20\mathrm{m}/\mathrm{s}$. The force exerted on the vertical wall just in front of the tube which stops water horizontally flowing out of the tube, i …

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 $\frac{3\mathrm{L}}{\alpha }\mathrm{m}$. The value of $\alpha$ is ........... (whe …

Sand is being dropped from a stationary dropper at a rate of $0.5{\mathrm{kgs}}^{-1}$ on a conveyor belt moving with a velocity of $5{\mathrm{ms}}^{-1}$. The power needed to keep belt moving with the same velocity will be :

A ball of mass 0.15 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 N, calculate the time duration of the contact of ball with the wall.

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:

Two billiard balls of mass 0.05 kg each moving in opposite directions with $10{\mathrm{ms}}^{-1}$ collide and rebound with the same speed. If the time duration of contact is $\mathrm{t}=0.005\mathrm{s}$, then what is the force exerted on the ball due to each other?