Consider two particles 1 and 2 moving with constant velocities v → 1 and v → 2 . If r → 1 and r → 2 are the radius vectors of the particles at the start, the relation between r → 1 , r → 2 , v → 1 and v → 2 when the two particles collide is

r → 1 - r → 2 r → 1 - r → 2 = v → 2 - v → 1 v → 2 - v → 1

r → 1 - r → 2 = v → 2 - v → 1

r → 1 + r → 2 r → 1 + r → 2 = v → 1 + v → 2 v → 1 + v → 2

r → 1 + r → 2 = v → 1 + v → 2

A body A of mass m is moving in a circular orbit of radius R about a planet. Another body B of mass m 2 collides with A with a velocity which is half v → 2 the instantaneous velocity v → of A. The collision is completely inelastic. Then, the combined body:

starts moving in an elliptical orbit around the planet

continues to move in a circular orbit

Escapes from the Planet's Gravitational field

Falls vertically downwards towards the planet

HARD

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Three spherical balls having mass $m_{1}, m_{2}$ and $m_{3}$ are placed one on top of another with their centre of masses aligned as shown in the figure below.

These balls are dropped together from height $H$ . The radii of balls are negligibly small in comparison with height $H$ . The heights to which the masses will rebound is expressed as $H_{r} = χ H$ . Assuming that all collisions (including the collision between $m_{1}$ and the floor) are elastic and $m_{1} ≫ m_{2} ≫ m_{3}$ , the values of $χ$ for masses $m_{1}, m_{2} and m_{3}$ .

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Important Questions on Laws of Motion

EASY

Physics>Mechanics>Laws of Motion>Collisions

During inelastic collision between two objects, which of the following quantity always remains conserved?

EASY

Physics>Mechanics>Laws of Motion>Collisions

On a frictionless surfaces, a block of mass

M

moving at speed

v

collides elastically with another block of same mass

M

which is initially at rest. After collision the first block moves at an angle

θ

to its initial direction and has a speed

\frac{v}{3}

. The second block's speed after the collision is:

HARD

Physics>Mechanics>Laws of Motion>Collisions

A particle of mass m is projected with a speed u from the ground at an angle

θ = \frac{π}{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

u \hat{i} .

The horizontal distance covered by the combined mass before reaching the ground is:

EASY

Physics>Mechanics>Laws of Motion>Collisions

Blocks of masses

m, 2 m, 4 m

and

8 m

are arranged in a line of a frictionless floor. Another block of mass

m

, moving with speed

υ

along the same line (see figure) collides with mass

m

in perfectly inelastic manner. All the subsequent collisions are also perfectly inelastic. By the time the last block of mass

8 m

starts moving the total energy loss is

p %

of the original energy. Value of

p

is close to:
Question Image

HARD

Physics>Mechanics>Laws of Motion>Collisions

A small particle of mass

m

moving inside a heavy, hollow and straight tube along the tube axis, undergoes elastic collision at two ends. The tube has no friction and it is closed at one end by a flat surface while the other end is fitted with a heavy movable flat piston as shown in figure. When the distance of the piston from closed end is

L = L_{0}

the particle speed is

v = v_{0} .

The piston is moved inward at a very low speed

V

such that

V ≪ \frac{d L}{L} v_{0},

where

d L

is the infinitesimal displacement of the piston. Which of the following statement(s) is/are correct?

Question Image

MEDIUM

Physics>Mechanics>Laws of Motion>Collisions

Particle

A

of mass

m_{1}

moving with velocity

(\sqrt{3} \hat{i} + \hat{j}) {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 respectively. If

m_{1} = 2 m_{2}

and after collision

{\vec{v}}_{1} - (\hat{i} + \sqrt{3} \hat{j}) {ms}^{- 1}

, the angle between

{\vec{v}}_{1}

and

{\vec{v}}_{2}

is :

MEDIUM

Physics>Mechanics>Laws of Motion>Collisions

Two particles of equal mass

m

have respective initial velocities

u \hat{i}

and

u (\frac{\hat{i} + \hat{j}}{2})

. They collide completely inelastically. The energy lost in the process is:

MEDIUM

Physics>Mechanics>Laws of Motion>Collisions

A ball of mass

1 kg

moving along

X

-direction collides elastically with a stationary ball of mass

m

. The first ball (mass

= 1 kg

) recoils at right angle to its original direction of motion. If the second ball starts moving at an angle

30 °

with the

X

-axis, the value of

m

must be

EASY

Physics>Mechanics>Laws of Motion>Collisions

A block of mass

m

moving on a frictionless surface at speed

v

collides elastically with a block of same mass, initially at rest. Now the first block moves at an angle

θ

with its initial direction and has speed

v_{1}

. The speed of the second block after the collision is

HARD

Physics>Mechanics>Laws of Motion>Collisions

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 the ground with a speed of

\sqrt{2 g h} .

If they collide head-on completely inelastically, the time taken for the combined mass to reach the ground, in units of

\sqrt{\frac{h}{g}}

is:

MEDIUM

Physics>Mechanics>Laws of Motion>Collisions

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 velocities of the two bodies (in degree) is -

HARD

Physics>Mechanics>Laws of Motion>Collisions

A tennis ball is dropped on a horizontal smooth surface. It bounces back to its original position after hitting the surface. The force on the ball during the collision is proportional to the length of compression of the ball. Which one of the following sketches describes the variation of its kinetic energy

K

with

t

time most appropriately? The figures are only illustrative and not to the scale.

MEDIUM

Physics>Mechanics>Laws of Motion>Collisions

Two balls

A

and

B

of masses

50 kg

and

20 kg

are moving in a straight line in the same direction at speed of

9 km h^{- 1}

and

18 km h^{- 1}

respectively. Ball

B

hits

A

and reverses its direction at a speed of

27 km h^{- 1} .

The speed of the ball

A

after the collision is

MEDIUM

Physics>Mechanics>Laws of Motion>Collisions

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 m s^{- 1}

in the horizontal direction just before the collision then the kinetic energy just before the combined system strikes the floor, is [Take

g = 10 m s^{- 2}

. Assume there is no rotational motion and loss of energy after the collision is negligible.]

EASY

Physics>Mechanics>Laws of Motion>Collisions

A metal ball of mass

2 kg

moving with a speed of

10 m s^{- 1}

had a head-on collision with a stationary ball of mass

3 kg

. If after collision, both the balls move together, then the loss in kinetic energy due to collision is

EASY

Physics>Mechanics>Laws of Motion>Collisions

Assertion (A): When we bounce a ball on the ground, it comes to rest after a few bounces, losing all its energy. This is an example of violation of conservation of energy.

Reason (R): Energy can change from one form to another but the total energy is always conserved.

Which of the following is true?

HARD

Physics>Mechanics>Laws of Motion>Collisions

Consider two particles

1

and

2

moving with constant velocities

{\vec{v}}_{1}

and

{\vec{v}}_{2}

. If

{\vec{r}}_{1}

and

{\vec{r}}_{2}

are the radius vectors of the particles at the start, the relation between

{\vec{r}}_{1}, {\vec{r}}_{2}, {\vec{v}}_{1}

and

{\vec{v}}_{2}

when the two particles collide is

MEDIUM

Physics>Mechanics>Laws of Motion>Collisions

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

(\frac{\vec{v}}{2})

the instantaneous velocity

\vec{v}

of A. The collision is completely inelastic. Then, the combined body:

HARD

Physics>Mechanics>Laws of Motion>Collisions

A body

A

of mass

m = 0.1 k g

has an initial velocity of

3 \hat{i} m s^{- 1}

. It collides elastically with another body

B

of the same mass which has an initial velocity of

5 \hat{j} m s^{- 1}

. After the collision,

A

moves with a velocity

\vec{v} = 4 (\hat{i} + \hat{j}) m s^{- 1}

. The energy of

B

after the collision is written as

\frac{x}{10} J

. The value of

x

HARD

Physics>Mechanics>Laws of Motion>Collisions

A simple pendulum, made of a string of length

l

and

a

bob of mass

m,

is released from a small angle

θ_{0} .

It strikes a block of mass

M,

kept on horizontal surface at its lowest point of oscillations, elastically. It bounces back and goes up to an angle

θ_{1} .

Then

M

is given by:

Important Questions on Laws of Motion

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