A hollow sphere of mass `M` lies on a rough horizontal plane when a particle of mass `m` traveling with speed `v` collides and sticks with it. If line of motion of the particle is at height `h` above the center of sphere, find `h` if the body rolls without slipping after collision (`m lt lt M`).

Explanation

To solve the problem step by step, we will analyze the situation before and after the collision, applying the principles of conservation of angular momentum and the conditions for rolling without slipping.

### Step 1: Understand the Initial Conditions
A hollow sphere of mass \( M \) is at rest on a rough horizontal plane. A particle of mass \( m \) is moving with speed \( v \) and collides with the sphere at a height \( h \) above the center of the sphere.

### Step 2: Conservation of Angular Momentum
Since there are no external torques acting on the system, we can use the conservation of angular momentum about the center of the hollow sphere (point O).

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