A ball of mass 0.1 kg makes an elastic head - on collision with a ball of unknown mass, initially at rest. If the 0.1 kg ball rebounds at one third of its original speed. What is the mass of the other ball?

0.3 kg

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0.1 kg

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0.2 kg

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0.4 kg

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Solution

The correct option is C 0.2 kg
Since collision is elastic relative velocity of approach
$=$ relative velocity of separation
$n_{1} = v_{1} / 3 + u_{2}$
$u_{2} = 2 v_{1} / 3$
Conserving momentum
$m_{1} v_{1} = - m_{1} \frac{v_{1}}{3} + m_{2} v_{1} / 3$
$0.1 \frac{4 v_{1}}{3} = m_{2} 2 v_{1} / 3$
$m_{2} = 0.2 k g$

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A ball of mass 0.1 kg makes an elastic head - on collision with a ball of unknown mass, initially at rest. If the 0.1 kg ball rebounds at one third of its original speed. What is the mass of the other ball?

The correct option is C 0.2 kgSince collision is elastic relative velocity of approach = relative velocity of separation n1=v1/3+u2u2=2v1/3Conserving momentum m1v1=−m1v13+m2v1/30.14v13=m22v1/3m2=0.2 kg