A sphere of mass m and radius R is kept on a rough horizontal floor. Constant force Facts at the top point of sphere along tangent. If there is sufficient friction on the floor to support pure rolling then calculate acceleration of sphere.

Explanation

To solve the problem, we need to analyze the forces acting on the sphere and apply the concepts of rotational motion and pure rolling. Here’s a step-by-step solution:

### Step 1: Identify the Forces Acting on the Sphere
The forces acting on the sphere are:
- The applied force \( F \) acting at the top of the sphere along the tangent.
- The frictional force \( f \) acting at the bottom of the sphere, opposing the motion.
- The weight of the sphere \( mg \) acting downwards at its center of mass.
- The normal force \( N \) acting upwards at the center of mass.
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