Conservation of Momentum — JEE Main PYQs

A bag of sand of mass 9.8 kg is suspended by a rope. A bullet of 200 g travelling with speed $10{\mathrm{ms}}^{-1}$ gets embedded in it, then loss of kinetic energy will be

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 mutually perpendicular sides as origin, the magnitude of position vector of centre of mass of the syste …

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 $2{\mathrm{ms}}^{-1}$. The velocity of the running man was ____ ${\mathrm{ms}}^{-1}$ when he jumps into the car.

A batsman hits back a ball of mass 0.4 kg straight in the direction of the bowler without changing its initial speed of $15{\mathrm{ms}}^{-1}$. The impulse imparted to the ball is _____ Ns.

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 $30{\mathrm{ms}}^{-1}$ and $40{\mathrm{ms}}^{-1}$ respectively. The velocity of the third piece will be:

A block of metal weighing 2 kg is resting on a frictionless plane (as shown in figure). It is struck by a jet releasing water at a rate of $1{\mathrm{kg}\mathrm{s}}^{-1}$ and at a speed of $10{\mathrm{ms}}^{-1}$. Then, the initial acceleration of the block, in ${\mathrm{ms}}^{-2}$, w …

Two blocks of masses 10 kg and 30 kg are placed on the same straight line with coordinates $(0,0)\mathrm{cm}$ and ( $\mathrm{x},0$ ) 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 through which …

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)

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 speed $\frac{v}{3}$ and the bob just completes the vertical circle. The value of $v$ is ______ …

Two bodies of mass 1 kg and 3 kg have position vector $\hat{i}+2\hat{j}+\hat{k}$ and $-3\hat{i}-2\hat{j}+\hat{k}$ respectively. The magnitude of position vector of centre of mass of this system will be similar to the magnitude of vector :

The initial mass of a rocket is 1000 kg. Calculate at what rate the fuel should be burnt so that the rocket is given an acceleration of $20{\mathrm{ms}}^{-2}$. The gases come out at a relative speed of $500{\mathrm{ms}}^{-1}$ with respect to the rocket :[Use …

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 $30^{\circ }$ with the original direction. The ratio of velocities of the balls after collision is $x:y$, where $x$ is ______.

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 direction perpendicular to the rod. The collision is completely elastic. After collision, particle c …

A circular hole of radius $\left(\frac{a}{2}\right)$ is cut 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:

If the kinetic energy of a moving body becomes four times its initial kinetic energy, then the percentage change in its momentum will be :

A bullet of 10 g , moving with velocity v , collides head-on with the stationary bob of a pendulum and recoils with velocity $100\mathrm{m}/\mathrm{s}$. The length of the pendulum is 0.5 m and mass of the bob is 1 kg . The minimum value of $\mathrm{v}=$ ____ …

A bullet of ' 4 g ' mass is fired from a gun of mass 4 kg . If the bullet moves with the muzzle speed of $50{\mathrm{ms}}^{-1}$, the impulse imparted to the gun velocity of recoil of gun are :

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 given by $\left(0,\frac{xR}{\pi }\right)$. Then, the value of $|x|$ is ______.

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 elastically with another body ' Q ' having mass ' $m$ ' initially at rest. If …

A block moving horizontally on a smooth surface with a speed of $40\mathrm{m}/\mathrm{s}$ splits into two parts with masses in the ratio of $1:2$. If the smaller part moves at $60\mathrm{m}/\mathrm{s}$ in the same direction, then the fractional change in kinetic en …

A body of mass M moving at speed ${\mathrm{V}}_0$ collides elastically with a mass ' m ' at rest. After the collision, the two masses move at angles ${\theta }_1$ and ${\theta }_2$ with respect to the initial direction of motion of the body of mass M . The largest possible va …

A block moving horizontally on a smooth surface with a speed of $40{\mathrm{ms}}^{-1}$ splits into two equal parts. If one of the parts moves at $60{\mathrm{ms}}^{-1}$ in the same direction, then the fractional change in the kinetic energy will be $x:4$ where $x=$ _____.

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 of $9\mathrm{m}/\mathrm{s}$ and makes an elastic collision with it. Thereafter B makes a com …

Two billiard balls of equal mass 30 g strike a rigid wall with same speed of 108 kmph (as shown) but at different angles. If the balls get reflected with the same speed then the ratio of the magnitude of impulses imparted to ball 'a' and ball 'b' by the wall along 'X' direction i …

A body of mass 2 kg moving with a speed of $4\mathrm{m}/\mathrm{s}$. makes an elastic collision with another body at rest and continues to move in the original direction but with one fourth of its initial speed. The speed of the two body centre of mass is …

A particle of mass M originally at rest is subjected to a force whose direction is constant but magnitude varies with time according to the relation


Where $F_0$ and $T$ are constants. The force acts only for the ti …

A ball of mass 10 kg moving with a velocity $10\sqrt{3}{\mathrm{ms}}^{-1}$ along $\mathrm{X}-$ axis, hits another ball of mass 20 kg which is at rest. After collision, the first ball comes to rest and the second one disintegrates into two equal pieces. One of the pieces star …

A large block of wood of mass $\mathrm{M}=5.99\mathrm{kg}$ is hanging form two long massless cords. A bullet of mass $\mathrm{m}=$ 10 g is fired into the block and gets embedded in it. The (block + bullet) then swing upwards, their centre of mass rising a vertical distance …

An object of mass $m_1$ collides with another object of mass $m_2$, which is at rest. After collision the objects move with equal speeds in the opposite direction. The ratio of the masses $m_2$ : $m_1$ is :

The projectile motion of a particle of mass $5g$ is shown in the figure. The initial velocity of the projectile is $5\sqrt{2}{\mathrm{ms}}^{-1}$ and air resistance is assumed to be negligible. The magnitude of change in momentum between the points A to B is …

Two identical blocks $A$ and $B$ each of mass $m$ resting on the smooth horizontal floor are connected by a light spring of natural L and spring constant K.
$A$ third block $C$ of mass $m$ moving with a speed $v$ along the line joining $A$ and $B$ collides with $A$. The maximum c …

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 the position $\frac{\mathrm{x}}{3}\frac{\mathrm{a}}{\pi },\frac{\mathrm{x}}{3}\frac{\mathrm{a}}{\pi }$ where $x$ is--------. (Roun …

A ball of mass 10 kg, moving with a velocity $10\sqrt{3}\mathrm{m}/\mathrm{s}$ along the x-axis, hits another ball of mass 20 kg which is at rest. After the collision, first ball comes to rest while second ball disintegrates into two equal pieces. One piece starts moving a …

Three point particles of masses $1.0\text{kg}$, $1.5\text{kg}$ and $2.5\text{kg}$ are placed at three corners of a right angle triangle of sides $4.0\text{cm}$, $3.0\text{cm}$ and $5.0\text{cm}$ as shown in the figure. The centre of mass of the system is at a point:

A satellite of mass $m$ is launched vertically upwards with an initial speed $u$ from the surface of the earth. After it reaches height $R$ ($R=$ radius of the earth), it ejects a rocket of mass $\frac{m}{10}$ so that subsequently the satellite moves in a circular orbit. The kin …

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

A body A , of mass $\mathrm{m}=0.1\mathrm{kg}$ has an initial velocity of $3\hat{\mathrm{i}}{\mathrm{ms}}^{-1}$. It collides elastically with another body, $B$ of the same mass which has an initial velocity of $5\hat{j}{\mathrm{ms}}^{-1}$. After collision, A moves with …

A particle of mass $m$ is dropped from a height $h$ above the ground. At the same time another particle of same mass is thrown vertically upwards from the ground with a speed of $\sqrt{2\mathrm{gh}}$.
If they collide head-on completely inelastically, the time taken for the combi …

As shown in figure when a spherical cavity (centered 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 sphere is at G, i.e. on the surface of the cavity. R can be determined by the equation:

A particle of mass $m$ is projected with a speed $u$ form the ground at an angle $\theta =\frac{\pi }{3}$ w.r.t. horizontal (x-axis). When it has reached its maximum height, it collides completely inelastically with another particle of the same mass and velocity uî. The horiz …

A rod of length $L$ has non-uniform linear mass density given by $\rho (x)=a+b{\left(\frac{x}{L}\right)}^2$, where $a$ and $b$ are constants and $0\le x\le L$. The value of $x$ for the centre of mass of the rod is at:

Two particles of equal mass 'm' have respective initial velocities $u\hat{i}$ and $u\left(\frac{\hat{i}+\hat{j}}{2}\right)$. They collide completely inelastically. The energy lost in the process is:

A body A of mass m is moving in a circular orbit of radius R about a planet. Another body B of mass $\frac{m}{2}$ collides with A with a velocity which is half $\left(\frac{\vec{v}}{2}\right)$ the instantaneous velocity $\vec{v}$ of A. The collision is completely inelastic. Then, …

A spaceship in space sweeps stationary interplanetary dust. As a result, its mass increases at a rate $\frac{dM(t)}{dt}=b{v}^2(t)$, where $v(t)$ its instantaneous velocity. The instantaneous acceleration of the satellite is:

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 mass 0.1 kg moving in a straight line with velocity $80\mathrm{m}/\mathrm{s}$ hits the rod at its bottom most point and sticks to …

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 $20\mathrm{m}/\mathrm{s}$ in the horizontal direction just before the combined system strikes the floo …

Particle $A$ of mass $m_1$ moving with velocity $(\sqrt{3}\hat{i}+\hat{j}){\mathrm{ms}}^{-1}$ collides with another particle $B$ of mass $m_2$ which is at rest initially. Let ${\vec{V}}_1$ and ${\vec{V}}_2$ be the velocities of particles $A$ and $B$ after collision respective …

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

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 final speed which is half of their initial speed. The angle between the initial velocities of the two …

Blocks of masses $\mathrm{m}$, $2\mathrm{m}$, $4\mathrm{m}$ and $8\mathrm{m}$ are arranged in a line on a frictionless floor. Another block of mass $\mathrm{m}$, moving with speed $v$ along the same line (see figure) collides with mass $\mathrm{m}$ in perfectly inelastic manne …