Answer
(a) A solid sphere will reach the bottom before the cylinder.
(b) A solid sphere will have a greater speed at the bottom.
(c) Both objects have the same total kinetic energy.
(d) The cylinder has a greater rotational kinetic energy
Work Step by Step
(a) A solid sphere will reach the bottom before the cylinder because the moment of inertia of a solid sphere is less than the moment of inertia of a cylinder. Therefore, a cylinder puts more energy into the rotational kinetic energy but a solid sphere will have more translational kinetic energy, and thus a faster speed at each moment.
(b) A solid sphere will have a greater speed at the bottom because the moment of inertia of a solid sphere is less than the moment of inertia of a cylinder. Therefore, a cylinder puts more energy into the rotational kinetic energy but a solid sphere will have more translational kinetic energy.
(c) Both objects have the same total kinetic energy. Initially, both objects have the same amount of potential energy and all this energy is transformed into kinetic energy.
(d) The cylinder has a greater rotational kinetic energy because the total energy for both objects is the same, but the translational kinetic energy of the cylinder is less because the cylinder's speed is less than the solid sphere's speed.
