A solid sphere rolls without slipping on a rough horizontal floor, moving with a speed `v`. It makes an elastic collision with a smooth vertical wall. After impact

Options

A. (a)it will move with a speed `v` initial
B. (b)its motion will be rolling with slipping initially and its rotational motion will stop momentarily at some instant.
C. (c)its motion will be rolling without slipping only after some time
D. (d)all of the above.

Explanation

To solve the problem of a solid sphere rolling without slipping on a rough horizontal floor and making an elastic collision with a smooth vertical wall, we can break down the situation step by step.

### Step 1: Understand the Initial Conditions
- The solid sphere is rolling without slipping with a speed \( v \).
- The angular velocity \( \omega \) of the sphere is related to its translational speed by the equation:
\[ v = r \omega \]
...