A uniform sphere is place on a smooth horizontal surface and as horizontal force F is appied on it at a distance h above the surface. The acceleratioin of the centre

Options

A. is maximum when h=0
B. is maximum when h=R
C. is maximum when h=2R
D. is independent of h

Answer

To solve the problem, we need to analyze the situation where a uniform sphere is placed on a smooth horizontal surface and a horizontal force \( F \) is applied at a distance \( h \) above the surface. We want to determine the acceleration of the center of mass of the sphere.

### Step-by-Step Solution:

1. **Understand the Setup**:
- We have a uniform sphere on a smooth horizontal surface.
- A horizontal force \( F \) is applied at a height \( h \) above the surface.

2. **Identify the Forces**:
- The only horizontal force acting on the sphere is the applied force \( F \).
- There is no frictional force acting because the surface is smooth.

3. **Analyze Motion**:
- Since there is no friction, the sphere will not rotate; it will simply slide across the surface.
- The point of application of the force being at height \( h \) does not affect the horizontal motion because there is no friction to create a torque that would cause rotation.

4. **Apply Newton's Second Law**:
- According to Newton's second law, the acceleration \( a \) of the center of mass of the sphere is given by:
\[ a = \frac{F}{m} \]
where \( m \) is the mass of the sphere.

5. **Conclusion**:
- The acceleration of the center of mass is independent of the height \( h \) at which the force is applied.
- Therefore, the final answer is:
\[ a = \frac{F}{m} \]