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A ball of mass m makes a head on elastic collision with a second ball (at rest) and rebounds with a speed equal to one – fourth of its original speed. What is the mass of the second ball?

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(3/5) m

(1/3) m

(7/3) m

(5/3)m

answer is D.

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Detailed Solution

Conservation of the momentum $m_{1} v_{1} + m_{2} v_{2} = m_{1} v_{1}' + m_{2} v_{2}' ∵ v_{1}' = - \frac{v_{1}}{4}$

$m v_{1} = m (\frac{- v_{1}}{4}) + m_{2} v_{2}' m_{2} v_{2}' = 5 m \frac{v_{1}}{4}$

$\begin{array}{l} v_{1} - v_{2} = v_{2}' - v_{1}' \\ v_{2}' = v_{1} + v_{1}' = \frac{3 v_{1}}{4} \end{array} ∴ m_{2} = \frac{5 m}{3}$

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