A solid sphere of radius R is placed on smooth horizontal surface. A horizontal force F is applied at height h from the lowest point. For the maximum acceleration of centre of mass, which is correct?

When a solid sphere is put on a smooth horizontal plane and a horizontal force is applied, the position where the force has been applied varies with the motion of the ball. The applied force can make both linear motion of the centre of mass and rotational motion about the center.
As the result of this, the effect of rotation will depend upon the height at which the force has been applied. If the force is applied above the center of the sphere, it creates torque and causes rotation. This decreases the fraction of the force that can be used to accelerate the center of mass linearly. On the other hand, if the force is applied lower on the sphere, closer to its base, the torque is smaller, and a greater fraction of the applied force contributes to linear acceleration.

The linear acceleration of the sphere can be maximized only when the torque is at its minimum. This occurs when the force is applied at the lowest point of the sphere. In this case, the force passes directly through the center of mass of the sphere, meaning there is no rotation and all of the force applied will be utilized for linear acceleration.

Therefore, the maximum acceleration of the center of mass of the sphere occurs when the horizontal force is applied at the lowest point on the sphere.

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