Question

A uniform sphere of radius $R$ is placed on a smooth horizontal surface and a horizontal force $F$ is applied on it at a distance $h$ above the centre. The acceleration of the centre of mass of the sphere is

• A. maximum when h $=$ 0
• B. maximum when h $=$ R
• C. maximum when h $=$ R/2
• D. independent of h

Answer 1

The correct option is D independent of h

Centre of mass of the uniform sphere lies at the centre of the sphere.
According to the question the force $F$ is applied at a distance $h$ from the centre.
Now this force will move and rotate the sphere simultaneously, (rotation is about the centre of mass) .
Here this force causes the centre of mass to accelerate in the direction of application.
The point of application of the force does not affect the acceleration, it will have same effect even when the force is applied at the centre or at a distance $R,$ it affects the angular acceleration of the sphere ( about the centre of mass) because Torque $(\tau =r\times F)$ where $r$ is the distance from centre of mass,
Hence the acceleration of centre of mass is independent of the point of application of force.