## Numerical

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...

A solid sphere of mass $$1 \mathrm{~kg}$$ rolls without slipping on a plane surface. Its kinetic energy is $$7 \times 10^{-3} \mathrm{~J}$$. The speed...

A particle of mass 100 g is projected at time t = 0 with a speed 20 ms$$^{-1}$$ at an angle 45$$^\circ$$ to the horizontal as given in the figure. The...

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...

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{...

The position vector of 1 kg object is $$\overrightarrow r = \left( {3\widehat i - \widehat j} \right)m$$ and its velocity $$\overrightarrow v = \lef...

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...

A rolling wheel of 12 kg is on an inclined plane at position P and connected to a mass of 3 kg through a string of fixed length and pulley as shown in...

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...

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 ...

Consider a badminton racket with length scales as shown in the figure.If the mass of the linear and circular portions of the badminton racket are same...

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...

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...

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...

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...

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...

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...

A force $$\overrightarrow F $$ = $${4\widehat i + 3t\widehat j + 4\widehat k}$$ is applied on an intersection point of x = 2 plane and x-axis. The mag...

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, ...

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 ...

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...

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...

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...

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...

A particle of mass 200 MeV/c2 collides with a
hydrogen atom at rest. Soon after the collision
the particle comes to rest, and the atom
recoils and goe...

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...

## MCQ (Single Correct Answer)

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...

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{...

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...

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...

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...

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

The torque of a force $$5 \hat{i}+3 \hat{j}-7 \hat{k}$$ about the origin is $$\tau$$. If the force acts on a particle whose position vector is $$2 i+2...

Two bodies of mass $$1 \mathrm{~kg}$$ and $$3 \mathrm{~kg}$$ have position vectors $$\hat{i}+2 \hat{j}+\hat{k}$$ and $$-3 \hat{i}-2 \hat{j}+\hat{k}$$ ...

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 ...

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...

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...

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 ...

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...

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...

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...

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 kgs$$-$$1...

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...

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

If force $$\overrightarrow F = 3\widehat i + 4\widehat j - 2\widehat k$$ acts on a particle position vector $$2\widehat i + \widehat j + 2\widehat k$...

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 $...

Angular momentum of a single particle moving with constant speed along circular path :

Moment of inertia of a square plate of side l about the axis passing through one of the corner and perpendicular to the plane of square plate is given...

A particle of mass m is suspended from a ceiling through a string of length L. The particle moves in a horizontal circle of radius r such that $$r = {...

List-I
List-II
(a) MI of the rod (length L, Mass M, about an axis $$ \bot $$ to the rod passing through the midpoint)
(i)...

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...

The figure shows two solid discs with radius R and r respectively. If mass per unit area is same for both, what is the rtaio of MI of bigger disc arou...

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...

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...

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

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...

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...

A triangular plate is shown. A force $$\overrightarrow F $$ = 4$$\widehat i$$ $$-$$ 3$$\widehat j$$ is applied at point P. The torque at point P with ...

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...

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...

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...

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
...

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...

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...

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...

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...

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)...

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...

A solid sphere of mass M and radius R is divided into two unequal parts. The first part has a mass of $${{7M} \over 8}$$
and is converted into a unifo...

The time dependence of the position of a particle of mass m = 2 is given by $$\overrightarrow r \left( t \right) = 2t\widehat i - 3{t^2}\widehat j$$
....

A thin disc of mass M and radius R has mass
per unit area $$\sigma $$(r) = kr2 where r is the distance
from its centre. Its moment of inertia about an...

A particle of mass m is moving along a
trajectory given by
x = x0 + a cos$$\omega $$1t
y = y0 + b sin$$\omega $$2t
The torque, acting on the particle ...

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...

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...

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
...

A ball is thrown vertically up (taken as +z-axis)
from the ground. The correct momentum-height
(p-h) diagram is :

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...

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...

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...

The position vector of the centre of mass $$\overrightarrow r {\,_{cm}}\,$$ of an asymmetric uniform bar of negligible area of crosssection as shown i...

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...

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...

A rigid massless rod of length 3l has two masses attached at each end as shown in the figure. The rod is pivoted at point P on the horizontal axis (se...

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...

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...

A force of $$40$$ $$N$$ acts on a point $$B$$ at the end of an $$L$$-shaped object, as shown in the figure. The angle $$\theta $$ that will produce ma...

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...

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...

Statement - 1 : Two particles moving in the same direction do not lose all their energy in a completely inelastic collision.
Statement - 2 : Princip...

The figure shows the position$$-$$time $$(x-t)$$ graph of one-dimensional motion of body of mass $$0.4$$ $$kg.$$ The magnitude of each impulse is
...

A player caught a cricket ball of mass $$150$$ $$g$$ moving at a rate of $$20$$ $$m/s.$$ If the catching process is completed in $$0.1s,$$ the force ...

A bomb of mass $$16kg$$ at rest explodes into two pieces of masses $$4$$ $$kg$$ and $$12$$ $$kg.$$ The velocity of the $$12$$ $$kg$$ mass is $$4\,\,m{...

A mass $$'m'$$ moves with a velocity $$'v'$$ and collides inelastically with another identical mass. After collision the $${1^{st}}$$ mass moves with ...

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 $$144$$ $$N$$ ...

## MCQ (More than One Correct Answer)

A particle of mass m is moving along the
side of a square of side ‘a’, with a uniform
speed v in the x-y plane as shown in the
figure :
Which of the ...