A solid sphere is rolling purely on a rough horizontal surface (coefficient of kinetic friction = $μ)$ with speed of centre u, as shown in the figure. It collides with a smooth vertical wall, the coefficient of restitution being ½. Choose the correct options.

Speed of C.O.M just after collision is $\frac{u}{2}$ .

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Friction acts rightward just after collision

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Angular velocity does not change during collision

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The speed of the centre of the sphere when it begins pure rolling does not depend on $μ$ .

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Solution

The correct options are
A
Speed of C.O.M just after collision is $\frac{u}{2}$ .

B
Friction acts rightward just after collision

C
Angular velocity does not change during collision

D
The speed of the centre of the sphere when it begins pure rolling does not depend on $μ$ .

Bottom pt is slipping leftward after collision hence friction will be rightward.

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A solid sphere is rolling purely on a rough horizontal surface (coefficient of kinetic friction = μ) with speed of centre u, as shown in the figure. It collides with a smooth vertical wall, the coefficient of restitution being ½. Choose the correct options.

A solid sphere is rolling purely on a rough horizontal surface (coefficient of kinetic friction = $μ)$ with speed of centre u, as shown in the figure. It collides with a smooth vertical wall, the coefficient of restitution being ½. Choose the correct options.