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If a ball moving with velocity u overtakes another ball of twice its own mass moving with one-seventh of its velocity and if the coefficient of restitution between them is $\frac{3}{4}$ , the velocity of the first ball after striking the second ball is:

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$\frac{u}{7}$

zero

$\frac{u}{4}$

$\frac{3 u}{4}$

answer is B.

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Detailed Solution

From Conservation of momentum,

$m (u) + 2 m (\frac{u}{7}) = m (v_{1}) + 2 m (v_{2})$

If coefficient of restitution is e , then

$e = \frac{v_{2} - v_{1}}{u_{1} - u_{2}} \Rightarrow \frac{3}{4} = \frac{v_{2} - v_{1}}{u - \frac{u}{7}}$

After solving we get:
$v_{1} = 0$

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