A hollow sphere of radius R rests on a smooth horizontal surface. It is pulled by a horizontal force acting tangentially at the highest point. Determine the distance travelled by the sphere during the time it completes one full rotation.

Step-by-step solution

Let the mass of the hollow sphere be m and the applied horizontal force be F . The linear acceleration of the center of mass is given by Newton's second law: a = F m The torque acting about the center of mass due to the force at the highest point is: = F R The moment of inertia of a hollow sphere about its center of mass is I = 2 3 mR^2 . The angular acceleration is: = I = FR 2 3 mR^2 = 3F 2mR Using the kinematic equations for linear and angular motion starting from rest, the distance travelled s and the angular di