A spherical ball of mass m and radius r rolls without slipping on a rough concave surface of large radius R. It makes small oscillations about the lowest point. Find the time period.

Explanation

To find the time period of small oscillations of a spherical ball of mass \( m \) and radius \( r \) rolling without slipping on a rough concave surface of large radius \( R \), we can follow these steps:

### Step-by-Step Solution:

1. **Understanding the System**:
- The ball rolls without slipping on a concave surface. When displaced by a small angle \( \theta \) from the vertical, the ball experiences gravitational force and friction.

2. **Forces Acting on the Ball**:
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