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A ball bounces to $80 %$ of its original height. What fraction of its potential energy is lost in each bounce?

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Important Questions on Centre of Mass, Momentum and Collisions

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Physics>Mechanics>Centre of Mass, Momentum and Collisions>Elastic and Inelastic Collisions

Two identical balls

A

and

B

having velocities of

0.5 m s^{- 1}

and

- 0.3 m s^{- 1}

, respectively, collide elastically in one dimension. The velocities of

B

and

A

after the collision, respectively, will be

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Physics>Mechanics>Centre of Mass, Momentum and Collisions>Elastic and Inelastic Collisions

In an inelastic collision, which of the following is true?

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Physics>Mechanics>Centre of Mass, Momentum and Collisions>Elastic and Inelastic Collisions

Two masses

m_{1}

and

m_{2}

moving with velocities

v_{1}

and

v_{2}

in opposite directions collide elastically and after collision

m_{1}

and

m_{2}

move with velocity

v_{2}

and

v_{1}

respectively. the ratio

v_{2} / v_{1}

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Physics>Mechanics>Centre of Mass, Momentum and Collisions>Elastic and Inelastic Collisions

Which one of the following is true for an elastic collision between two bodies?

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Physics>Mechanics>Centre of Mass, Momentum and Collisions>Elastic and Inelastic Collisions

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

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Physics>Mechanics>Centre of Mass, Momentum and Collisions>Elastic and Inelastic Collisions

A rubber ball is released from a height of

5 m

above the floor. It bounces back repeatedly, always rising to

\frac{81}{100}

of the height through which it falls. Find the average speed of the ball. (Take

g = 10 {m s}^{- 2}

)

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Physics>Mechanics>Centre of Mass, Momentum and Collisions>Elastic and Inelastic Collisions

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 $m ≪ M$ , body $Q$ will have a maximum speed equal to $2 u$ after collision.

Reason R : During elastic collision, the momentum and kinetic energy are both conserved.

In the light of the above statements, choose the most appropriate answer from the options given below:

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Physics>Mechanics>Centre of Mass, Momentum and Collisions>Elastic and Inelastic Collisions

This question has $Statement - I$ and $Statement - II$ of the four choices given after the Statements, choose the one that best describes the two Statements.

$Statement - I:$ A point particle of mass $m$ moving with speed $ν$ collides with stationary point particle of mass $M$ . If the maximum energy loss possible is given as
$f (\frac{1}{2} m ν^{2})$ then $f = (\frac{m}{M + m})$ .

$Statement - II:$ Maximum energy loss occurs when the particles get stuck together as a result of the collision.

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Physics>Mechanics>Centre of Mass, Momentum and Collisions>Elastic and Inelastic 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

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Physics>Mechanics>Centre of Mass, Momentum and Collisions>Elastic and Inelastic 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

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Physics>Mechanics>Centre of Mass, Momentum and Collisions>Elastic and Inelastic Collisions

A particle of mass

m

moving in the

x

direction with speed

2 v

is hit by another particle of mass

2 m

moving in the

y

direction with speed

v .

If the collision is perfectly inelastic, the percentage loss in the energy during the collision is close to:

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Physics>Mechanics>Centre of Mass, Momentum and Collisions>Elastic and Inelastic Collisions

A body of mass

m_{1}

moving with an unknown velocity of

v_{1} \hat{i},

undergoes a collinear collision with a body of mass

m_{2}

moving with a velocity

v_{2} \hat{i} .

After the collision,

m_{1}

and

m_{2}

move with velocities of

v_{3} \hat{i}

and

v_{4} \hat{i},

respectively. If

m_{2} = 0.5 m_{1}

and

v_{3} = 0.5 v_{1},

then

v_{1}

is:

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Physics>Mechanics>Centre of Mass, Momentum and Collisions>Elastic and Inelastic Collisions

An alpha- particle of mass

m

suffers

1 -

dimensional elastic collision with a nucleus at rest of unknown mass. It is scattered directly backwards losing

64 %

of its initial kinetic energy. The mass of the nucleus is

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Physics>Mechanics>Centre of Mass, Momentum and Collisions>Elastic and Inelastic 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:

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Physics>Mechanics>Centre of Mass, Momentum and Collisions>Elastic and Inelastic Collisions

A satellite of mass

M

is in a circular orbit of radius

R

about the center of the earth. A meteorite of the same mass, falling towards the earth, collides with the satellite completely inelastic. The speeds of the satellite and the meteorite are the same, just before the collision. The subsequent motion of the combined body will be:

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Physics>Mechanics>Centre of Mass, Momentum and Collisions>Elastic and Inelastic Collisions

A large number $(n)$ of identical beads, each of mass $m$ and radius $r$ are strung on a thin smooth rigid horizontal rod of length $L (L ≫ r)$ and are at rest at random positions. The rod is mounted between two rigid supports (see figure). If one of the beads is now given a speed $v$ , the average force experienced by each support after a long time is (assume all collisions are elastic):
Question Image

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Physics>Mechanics>Centre of Mass, Momentum and Collisions>Elastic and Inelastic Collisions

A block of mass $m = 10 kg$ rests on a horizontal table. The coefficient of friction between the block and the table is $0.05$ . When hit by a bullet of mass $50 g$ moving with speed $v$ , that gets embedded in it, the block moves and comes to stop after moving a distance of $2 m$ on the table. If a freely falling object were to acquire speed $\frac{v}{10}$ after being dropped from height $H$ , then neglecting energy losses and taking $g = 10 m s^{- 2}$ , the value of $H$ is close to

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Physics>Mechanics>Centre of Mass, Momentum and Collisions>Elastic and Inelastic 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?

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Physics>Mechanics>Centre of Mass, Momentum and Collisions>Elastic and Inelastic 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

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Physics>Mechanics>Centre of Mass, Momentum and Collisions>Elastic and Inelastic Collisions

A ball is thrown vertically downwards from a height of

20 m

with an initial velocity

v_{0}

. It collides with the ground, loses

50

percent of its energy in collision and rebounds to the same height. The initial velocity

v_{0}

is: (Take

g = 10 m s^{- 2}

)

A ball bounces to 80% of its original height. What fraction of its potential energy is lost in each bounce?

Important Questions on Centre of Mass, Momentum and Collisions

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A ball bounces to $80 %$ of its original height. What fraction of its potential energy is lost in each bounce?