In the figure shown, coefficient of restitution between A and B is $e = \frac{1}{2}$ , then

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Loss of kinetic energy during the collision is $\frac{3}{16} m v^{2}$

Loss of kinetic energy during the collision is $\frac{1}{4} m v^{2}$

Velocity of B after collision is $\frac{v}{2}$

Impulse between two during collision is $\frac{3}{4} m v$

answer is B, C.

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Detailed Solution

$∣ Impulse | = | Δ p_{1} or Δ p_{2} ∣$

$= m (\frac{3}{4} v) = \frac{3 m v}{4}$

Loss kinetic energy $= K_{i} - K_{f}$

$\begin{array}{l} = \frac{1}{2} m v^{2} - [\frac{1}{2} m {(\frac{3 v}{4})}^{2} + \frac{1}{2} m {(\frac{v}{4})}^{2}] \\ = \frac{3}{16} m v^{2} \end{array}$

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