A body A of mass M while falling vertically downwards under gravity breaks into two parts ; a body B of mass 1 3 M and body C of mass 2 3 M . The centre of mass of bodies B and C taken together shifts as compared to that of body A towards

depends on the height of breaking

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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Two bodies of mass $10 kg$ and $2 kg$ are moving with velocity $2 \hat{i} - 7 \hat{j} + 3 \hat{k} {ms}^{- 1}$ and $- 10 \hat{i} + 35 \hat{j} - 3 \hat{k} {ms}^{- 1}$ ,
respectively. The velocity of their centre of mass is

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Important Questions on Centre of Mass, Momentum and Collisions

HARD

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Alpha Question Bank for Medical: Physics>Chapter 9 - Centre of Mass, Momentum and Collisions>Exercise-1>Q 66

Consider a system of two particles having masses

m_{1}

and

m_{2} .

If the particle of mass

m_{1}

is pushed towards the mass centre of particles through a distance

d

, by what distance would the particle of mass

m_{2}

move so as to keep the mass centre of particles at the original position?

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Alpha Question Bank for Medical: Physics>Chapter 9 - Centre of Mass, Momentum and Collisions>Exercise-1>Q 67

Two identical particles move towards each other with velocity

2 v

and

v

respectively. This velocity of the centre of mass is -

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Alpha Question Bank for Medical: Physics>Chapter 9 - Centre of Mass, Momentum and Collisions>Exercise-1>Q 68

Two blocks of masses $10 kg, 4 kg$ are connected by a spring of negligible mass and placed on a frictionless horizontal surface. An Impulse gives a velocity of $14 m / s$ to the heavier block in the direction of the lighter block. The velocity of the centre of mass is:

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Alpha Question Bank for Medical: Physics>Chapter 9 - Centre of Mass, Momentum and Collisions>Exercise-1>Q 69

A body A of mass

M

while falling vertically downwards under gravity breaks into two parts ; a body

B

of mass

\frac{1}{3} M

and body

C

of mass

\frac{2}{3} M .

The centre of mass of bodies

B

and

C

taken together shifts as compared to that of body A towards

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Alpha Question Bank for Medical: Physics>Chapter 9 - Centre of Mass, Momentum and Collisions>Exercise-1>Q 70

Consider a two-particle system with the particles having masses

m_{1}

and

m_{2}

. 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?

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Alpha Question Bank for Medical: Physics>Chapter 9 - Centre of Mass, Momentum and Collisions>Exercise-1>Q 71

A uniform sphere is placed on a smooth horizontal surface and a horizontal force

F

is applied to it at a distance

h

above the surface. The acceleration of the centre

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Alpha Question Bank for Medical: Physics>Chapter 9 - Centre of Mass, Momentum and Collisions>Exercise-1>Q 72

A can of height

h

is filled with liquid of uniform density

ρ .

If the liquid is coming out from the hole in bottom then centre of mass of the "can

+

water in the can"

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Alpha Question Bank for Medical: Physics>Chapter 9 - Centre of Mass, Momentum and Collisions>Exercise-1>Q 73

A man of mass

M

stands at one end of a plank of length

L

which lies at rest on a frictionless horizontal surface. The man walks to the other end of the plank. If the mass of the plank is

\frac{M}{3}

, the distance that the man moves relative to the ground is

Two bodies of mass 10 kg and 2 kg are moving with velocity 2i^-7j^+3k^ ms-1 and -10i^+35j^-3k^ ms-1, respectively. The velocity of their centre of mass is

Important Questions on Centre of Mass, Momentum and Collisions

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Two bodies of mass $10 kg$ and $2 kg$ are moving with velocity $2 \hat{i} - 7 \hat{j} + 3 \hat{k} {ms}^{- 1}$ and $- 10 \hat{i} + 35 \hat{j} - 3 \hat{k} {ms}^{- 1}$ ,
respectively. The velocity of their centre of mass is