A solid sphere is rolling purely on a rough horizontal surface (coe...

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A solid sphere is rolling purely on a rough horizontal surface (coefficient of kinetic friction \( = \) \( \mu \) ) with speed of centre \( =u \). It collides inelastically
\( \mathrm{P} \) with a smooth vertical wall at a certain moment, the coefficient of restitution being \( \frac{1}{2} \). The sphere will begin pure rolling after a time
(1) \( \frac{3 u}{7 \mu g} \)
(2) \( \frac{2 u}{7 \mu g} \)
(3) \( \frac{3 u}{5 \mu g} \)
(4) \( \frac{2 u}{5 \mu g} \)
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