Coefficient of restitution

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Question

A sphere of mass 2 kg moving with velocity of 4 m/s collides head on with a stationary sphere of mass 4 kg during the course of collision, average impulse acting on the 4 kg sphere is 8 N-S. Then the coefficient of restitution is

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Solution

For 4 kg sphere, $4 V_{2} - 4 \times 0 = 8 \Rightarrow V_{2} = 2 \frac{m}{s}$
For 2 kg sphere, $2 \times V_{1} - 2 \times 4 = - 8 \Rightarrow V_{1} = 0 m / s$
$∴ e = \frac{V_{2} - V_{1}}{u_{1} - u_{2}} = \frac{2 - 0}{4 - 0} = \frac{1}{2}$

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