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What will be the ratio of the momentum required to stop two balls A and B of masses ' $m$ ' and ' $3 m$ ' at the same time when they are in motion with velocities ' $2 v$ ' and ' $3 v$ ' respectively?

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2 : 1

1 : 1

2 : 3

2 : 5

answer is A.

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Detailed Solution

the ratio of the momentum required to stop two balls A and B is

1 : 3

According to Newton's second law, force is the rate of change of momentum.
So, the ratio of forces will be,
Since the final velocities of the balls are zero. So the ratio of change of momentum of the balls will be

\frac{P 1}{P 2} = \frac{(0 - 2 mv)}{0 - 3 m \times 3 v}

\Rightarrow \frac{P 1}{P 2}

\frac{2}{1}

= 2:1

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