Two particles A and B move with constant velocities v 1 and v 2 . At the initial moment of their position vectors are r → 1 and r → 2 respectively. The condition for the particles A and B for their collision is

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

r → 1 - r → 2 = v → 1 - v → 2

r → 1 · v → 1 = r → 2 · v → 2

r → 1 × v → 1 = r → 2 × v → 2

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:

Such that it escapes to infinity

In a circular orbit of a different radius

In the same circular orbit of radius R

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 1 2 m ν 2 then f = m M + m . Statement - II: Maximum energy loss occurs when the particles get stuck together as a result of the collision.

Statement- I is false, Statement- II is true.

Statement- I is true, Statement- II is false.

Statement- I is true, Statement- II is true, Statement- II is a correct explanation of Statement- I .

Statement- I is true, Statement- II is true, Statement- II is not a correct explanation of Statement- I .

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Assertion : Position of centre of mass is independent of the reference frame:
Reason: Centre of mass is same for all bodies.

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Important Questions on Centre of Mass, Momentum and Collisions

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Alpha Question Bank for Medical: Physics>Chapter 9 - Centre of Mass, Momentum and Collisions>Exercise-2>Q 23

Assertion : The position of centre of mass of a body does not depend upon shape and size of the
body. Reason : Centre of mass of a body lies always at the centre of the body.

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Alpha Question Bank for Medical: Physics>Chapter 9 - Centre of Mass, Momentum and Collisions>Exercise-2>Q 24

Assertion : When a body dropped from a height explodes in mid air, its centre of mass keeps moving in vertically downward direction.

Reason : Explosion occur under internal forces only. External force is zero.

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Alpha Question Bank for Medical: Physics>Chapter 9 - Centre of Mass, Momentum and Collisions>Exercise-3>Q 1

A solid cylinder of mass

3 kg

is rolling on a horizontal surface with velocity

4 m s^{- 1}

. It collides with a horizontal spring of force constant

200 N m^{- 1}

. The maximum compression produced in the spring will be : ?

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Alpha Question Bank for Medical: Physics>Chapter 9 - Centre of Mass, Momentum and Collisions>Exercise-3>Q 2

A light rod of length I has two masses

m_{1}

and

m_{2}

attached to its two ends. The moment of inertia of the system about an axis perpendicular to the rod and passing through the centre of mass is

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Alpha Question Bank for Medical: Physics>Chapter 9 - Centre of Mass, Momentum and Collisions>Exercise-3>Q 3

Two particles

A

and

B

move with constant velocities

v_{1}

and

v_{2}

. At the initial moment of their position vectors are

{\vec{r}}_{1}

and

{\vec{r}}_{2}

respectively. The condition for the particles

A

and

B

for their collision is

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Alpha Question Bank for Medical: Physics>Chapter 9 - Centre of Mass, Momentum and Collisions>Exercise-3>Q 4

An explosion blows a rock into three parts. Two parts go off at right angles to each other. These two are,

1 kg

first part moving with a velocity of

12 m s^{- 1}

and

2 kg

second part moving with a velocity of

8 m s^{- 1}

. If the third part flies off with a velocity of

4 m s^{- 1}

, its mass would be:

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Alpha Question Bank for Medical: Physics>Chapter 9 - Centre of Mass, Momentum and Collisions>Exercise-3>Q 5

A ball moving with velocity

2 m s^{- 1}

collides head on with another stationary ball of double the mass. If the coefficient of restitution is

0.5

, then their velocities (in

m s^{- 1}

) after collision will be:

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Alpha Question Bank for Medical: Physics>Chapter 9 - Centre of Mass, Momentum and Collisions>Exercise-3>Q 6

Two particles which are initially at rest move towards each other under the action of their mutual attraction. If their speeds are

v

and

2 v

at any instant, then the speed of center of mass of the system is,

Assertion : Position of centre of mass is independent of the reference frame: Reason: Centre of mass is same for all bodies.

Important Questions on Centre of Mass, Momentum and Collisions

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Assertion : Position of centre of mass is independent of the reference frame:
Reason: Centre of mass is same for all bodies.