A ball $P$ of mass $2 k g$ undergoes an elastic collision with another ball Q at rest. After collision, ball $P$ continues to move in its original direction with a speed one–fourth of its original speed. What is the mass of ball Q?

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$1.8 k g$

$0.9 k g$

$1.2 k g$

$1.5 k g$

answer is B.

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Detailed Solution

Let mass of Q is $m$ and initially P was moving with speed $v$ and as direction of P is not changing this collision must be head on

After collisions, we use

$v_{1} = \frac{m_{1} - m_{2}}{m_{1} + m_{2}} u_{1} + \frac{2 m_{2}}{m_{1} + m_{2}} u_{2} \Rightarrow \frac{v}{4} = \frac{2 - m}{2 + m} v + 0 2 + m = 8 - 4 m 5 m = 6 m = 1.2 k g$

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