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Question

When two identical balls b1 and b2, which have equal masses are moving with velocities, V and 2V respectively, the ratio of inertia and momentum of b1 to b2 are:

A
2:1 and 1:2
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B
1:1 and 1:2
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C
1:1 and 1:1
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D
1:1 and 2:1
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Solution

The correct option is B 1:1 and 1:2
The inertia of a body depends on its mass.
As the balls have equal mass, the ball b1 and b2 have same inertia.
Let the mass of the balls be M.
I1 and I2 are the inertia of ball b1 and b2 respectively
I1 = K×M
I2 = K×M
where , K is constant and M is the mass of the ball.

Case 1: Ratio of inertia

I112=K×MK×M
⇒I112=11

Case 2: Ratio of momentum

Momentum is the product of mass and velocity, so the ball with greater velocity has greater momentum.
Let P1 and P2 be the momentum of b1 and b2 respectively.
Let V1 and V2 be the velocities of b1 and b2.
Given V1 = V and V2 = 2V
P1P2=M×VM×2V
⇒P1P2=12.

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