COM, Momentum &

Collision
Abhilash Sharma
B.Tech - NIT Calicut

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Code: ABHILASH
Code: ABHILASH
Code: ABHILASH
 COM,
Momentum &
Collision
Centre of Mass
Centre of Mass
Centre of Mass
Discrete Mass System
Centre of Mass
Discrete Mass System
[JEE Main 2019]
Centre of Mass
Continuous Body
Example
[JEE Main 2019]
Centre of Mass
Uniform & symmetric Continuous Body
Centre of Mass
Uniform & Asymmetric Continuous Body

Semicircular Wire
Centre of Mass
Semicircular Disc
Centre of Mass
Cone

Triangle
Centre of Mass

Hollow Sphere Solid Hemisphere

A uniform solid circular cone of base radius r is
joined to a uniform solid hemisphere of radius r
and of the same density, so as to have a common
face. The centre of mass of the composite solid
lies on the common face. The height of the cone is

A. 2r
B. √3r
C. 3r
D. √6r
Centre of Mass of Objects with Cavity
A circular hole of radius a/2 is cut out of a circular
disc of radius ‘a’ shown in figure. The centroid of
the remaining circular portion with respect to
point ‘O’ will be
[JEE Main 2021]
A. 10a/11
B. 2a/3
C. a/6
D. 5a/6
[JEE Main 2019]
Motion of Centre of Mass
Motion of Centre of Mass
Acceleration of Centre of Mass
[JEE Main 2019]
Acceleration of Centre of Mass
Acceleration of Centre of Mass
Example
Consider a two-particle system with the particles having masses m1
and m2 . If the first particle is pushed towards the centre of mass
through a distance d, by what distance should the second particle be
moved so as to keep the centre of mass at the same position ?
Block A of mass 5 kg is placed on top of a smooth
triangular block B having a mass of 30 kg. If the
system is released from rest, determine the
distance moved by B when A reaches the bottom.
Neglect the size of block A.

A. 1/12
B. 1/14
C. 1/16
D. 1/20
A projectile is fired at a speed of 100 m/s at an angle
of 37° above the horizontal. At the highest point, the
projectile breaks into two parts of mass ratio 1:3, the
smaller coming to rest. Find the distance from the
launching point to the point where the heavier piece
lands

A. 480 m
B. 960 m
C. 1120 m
D. 2250 m
A cart of mass 6kg is at rest on a frictionless
horizontal surface and a pendulum bob of mass 2 kg
hangs from the roof of the cart. The string breaks, the
bob falls on the floor, makes several collisions on the
floor and finally lands up in a small slot made in the
floor. The horizontal distance between the string and
the slot is 1 m. Find the displacement of the cart
during this process

A. 10 cm
B. 25 cm
C. 50 cm
D. 75 cm
Linear Momentum Conservation
Linear Momentum Conservation
A bullock cart of mass 200 kg is moving at a
speed of 10 km/h. As it overtakes a school boy
walking at a speed of 4 km/h, the boy sits on the
cart. If the mass of the boy is 25 kg, what will be
the new velocity of the bullock cart ?

A. 16/3 km/h
B. 25/3 km/h
C. 28/3 km/h
D. 32/3 km/h
A bullet of mass 50 g is fired horizontally into the
bob of mass 450 g of a long simple pendulum
with string length 2 m as shown in the figure. The
bullet remains inside the bob and the bob just
completes the vertical circular motion. Find the
speed of the bullet

A. 10 m/s
B. 100 m/s
C. 500 m/s
D. 1000 m/s
A bullet of mass 20 g travelling horizontally with a
speed of 500 m/s passes through a wooden block of
mass 10. 0 kg initially at rest on a level surface. The
bullet emerges with a speed of 100 m/s and the block
slides 20 cm on the surface before coming to rest.
Find the friction coefficient between the block and the
surface

A. 0.16
B. 0.32
C. 0.50
D. 0.72
A block of mass 2 kg is moving on a frictionless
horizontal surface with a velocity of 1 m/s towards
another block of equal mass kept at rest. The spring
constant of the spring fixed at one end is 100 N/m.
Find the maximum compression of the spring

A. 5 cm
B. 10 cm
C. 15 cm
D. 20 cm
Figure shows a small body of mass 2 kg placed over a
larger mass 8 kg whose surface is horizontal near the
smaller mass and gradually curves to become
vertical. The smaller mass is pushed on the longer
one at a speed 10 m/s and the system is left to itself.
Assume that all the surfaces are frictionless. Find the
maximum height (from the ground) that the smaller
mass ascends

A. 2m
B. 4m
C. 6m
D. 8m
Impulse
Impulse
A ball of mass m moving with velocity v
strikes the horizontal surface at an angle 𝞱.
Assuming no loss of energy, find the
Impulse imparted to the ball

A. 2 mv
B. 2mv cos𝞱
C. 2mv sin𝞱
D. mv
A block of mass m and a pan of equal mass are
connected by a string going over a smooth light
pulley as shown in figure. Initially the system is at
rest when a particle of mass m falls on the pan and
sticks to it. If the particle strikes the pan with a
speed v find the speed with which the system moves
just after the collision.

A. v/2
B. 3v
C. v/3
D. 2v
Collision
Collision
Types of Collision
Types of Collision
A ball of mass m moving with velocity 3v collides
head on with a stationary ball of mass M. The
velocity of both the balls become v after collision.
The value of M/m

A. 1
B. 2
C. 3
D. 4
Coefficient of Restitution (e)
Example
A ball dropped from height h collides with the floor and bounces up.
If the coefficient of restitution between ball and floor is e, find the
velocity with which the ball rises.
Completely Inelastic Collision
Inelastic Collision
(a) 2 (b) 3 (c) 4 (d) 5
Elastic Collision
Elastic Collision
An object of mass m collides elastically with another object of mass
M which is at rest. After the collision the objects move with equal
speeds in opposite direction. The ratio of the masses M/m is

(a) 3 (b) 2 (c) 1/2 (d) 1

Elastic Collision
Special Cases
The bob A of a simple pendulum is released when the string makes
an angle 45𝆩 with the vertical. At the bottom most point of its
trajectory it hits another bob B of same material and same mass
kept at rest on the table. Assuming no loss of energy
Elastic Collision
Special Cases
Collision in 2D
Collision in 2D
[JEE Main 2020]
Oblique Collision
Example
A ball of mass 2 grams hits the floor with a speed 10 m/s making an
angle of incidence 45° with the normal. The coefficient of restitution
is 1/√3. The speed and the angle of reflection of the ball are

(a) 10 m/s, 45° (b) 10√3/2 m/s, 60°

(c) 10√2 m/s, 30° (d) 10√2/3 m/s, 60°
As shown in the figure a body of mass m moving with
speed 3 m/s hits a smooth fixed incline plane and
rebounds with a velocity v in the horizontal direction. If
the angle of incline is 30𝆩 , then velocity v will be

(a) 3 (b) √3 (c) 1/√3 (d) Not possible

A ball is dropped on a smooth inclined plane and is
observed to move horizontally after the impact. The
coefficient of restitution between the plane and ball is e. If
the inclination of the plane is 𝞱, then the value of tan𝞱 is

(a) 1 (b) √e (c) e/2 (d) e

A small particle travelling with a velocity v=10 m/s collides
elastically with a spherical body of equal mass and of radius
r=5 m initially kept at rest. The centre of this spherical body is
located a distance 𝞺=4m away from the direction of motion of
the particle. Find the final velocity of the sphere.

(a) 10 m/s (b) 2m/s (c) 4m/s (d) 6m/s

Variable Mass System
Thrust Force
Example
A constant force F is applied on a trolley of initial mass m0 kept over a
smooth surface at rest. Sand is poured gently over the trolley at a
constant rate of µ kg/s. After time t, find the velocity of the trolley.
Example
A trolley of initial mass m0 is kept over a smooth surface as
shown in figure. A constant force F is applied on it. Sand kept
inside the trolley drains out from its floor at a constant rate of µ
kg/s. After time t find the velocity of the trolley
A uniform chain of mass m and length l hangs on a thread and
just touches the surface of a weighing scale by its lower end.
Find the reading of the scale when half of its length has fallen.
The fallen part does not form heap.
(a) mg/2 (b) mg (c) 3mg/2 (d) 2
Variable Mass System
Variable Mass System
Rocket Propulsion
Rocket Propulsion
Code: ABHILASH
Code: ABHILASH
Code: ABHILASH
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