The two balls A and B as shown in figure are of masses m and 2 m, respectively. The A moves with velocity u toward right while B is at rest. The wall is at extreme right is fixed. Coefficient of restitution for collision between 2 balls is $1/2$ & between ball & wall is 1. Then speed of A & B after all possible collisions are:

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v_{B} = \frac{u}{4}

v_{A} = \frac{u}{4}

v_{B} = \frac{u}{8}

v_{A} = \frac{u}{2}

answer is A, D.

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Detailed Solution

e = \frac{1}{2}

After A, B collision

$v_{A} = \frac{(m - \frac{m}{u^{2}}) u}{3 m} = 0$

$v_{B} = \frac{(1 + \frac{1}{2}) mu}{3 m} = \frac{u}{2} right$

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After B wall collision

$v_{A} = \frac{(1 + \frac{1}{2}) 2m (\frac{u}{2})}{3 m} = \frac{u}{2} left$

$v_{B} = \frac{(2m - \frac{m}{2}) (\frac{u}{2})}{3 m} = \frac{u}{4} left$

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