A uniform disc of radius R and mass M is free to rotate about a fixed horizontal axis perpendicular to its plane and passing through its centre. A string is wrapped over its rim and a block of mass m is attached to the free end of the string. The block is released from rest. If string does not slip on the rim then find the acceleration of the block. Neglect the mass of the string.

Explanation

To solve the problem, we will analyze the forces acting on the block and the torque acting on the disc. We will use Newton's second law and the rotational analog for the disc.

### Step-by-Step Solution:

1. **Identify the System**:
We have a uniform disc of mass \( M \) and radius \( R \) that can rotate about a fixed axis. A block of mass \( m \) is attached to a string wrapped around the rim of the disc.

2. **Define Variables**:
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