A horizontal force `F` is applied at a height `h` above the center of a solid cylinder of mass `m` and radius `R`. Determine friction, if cylinder rolls without slipping. For what value of `h`, friction is zero.

Explanation

To solve the problem, we will analyze the forces acting on the solid cylinder and apply the equations of motion for both translation and rotation. Here are the steps to derive the solution:

### Step 1: Identify the Forces Acting on the Cylinder
The forces acting on the cylinder are:
- The applied horizontal force \( F \).
- The frictional force \( f_r \) acting at the point of contact with the ground.
- The weight of the cylinder \( mg \) acting downwards at its center of mass.
- The normal force \( N \) acting upwards at the point of contact.
...