A force F acts tangentially at the highest point of a sphere of mass m kept on a rough horiozontal plane. If the sphere rolls withut slipping, find the accelerastioni of the centre of the sphere.

Explanation

To solve the problem of finding the acceleration of the center of a sphere of mass \( m \) rolling without slipping on a rough horizontal plane when a force \( F \) acts tangentially at the highest point, we can follow these steps:

### Step 1: Identify the forces acting on the sphere
- The force \( F \) acts tangentially at the highest point of the sphere.
- There is a frictional force \( f \) acting at the bottom point of the sphere, opposite to the direction of motion.

### Step 2: Write the equations of motion
1. **Translational motion**: The net force acting on the sphere in the horizontal direction gives us:
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