A hollow spherical shell of mass M and radius R is rolling without slipping on a rough horizontal floor with a constant speed v . It then enters a smooth horizontal section where it collides head-on with an ideal spring of force constant k attached to a vertical wall. The maximum compression of the spring is:

Step-by-step solution

When the hollow spherical shell enters the smooth horizontal section, the frictional force becomes zero. Consequently, there is no external torque acting on the shell about its center of mass, and its angular velocity remains constant. As the shell compresses the spring, the spring force acts horizontally through the center of mass, so it also produces no torque. Therefore, the rotational kinetic energy of the shell is conserved during the compression. Only the translational kinetic energy of the shell is converted