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A solid sphere rolls without slipping on a rough horizontal floor, moving with a speed \( \boldsymbol{v} . \) It makes an elastic collision with a smooth vertical wall. After impact, This question has multiple correct options

1. it will move with a speed \( v \) initially.
2. its motion will be rolling without slipping
3. its motion will be rolling with slipping initially and its rotational motion will stop momentarily at some instant.
4. its motion will be rolling without slipping only after some time.

Correct answer: it will move with a speed \( v \) initially.

Solution

Because the wall is smooth, it exerts no tangential impulse, so the sphere’s spin is unchanged during impact. For an elastic collision with a fixed wall, the center-of-mass speed immediately after impact has the same magnitude as before, so it moves away with speed v initially.

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