Question 8-16.

By conservation of energy, since both the sphere and cylinder are released from rest at the same level of the incline, the same amount of potential energy will be converted to kinetic energy when they reach the bottom. Hence they should they the same total kinetic energy.

Since both objects have the same mass, the one with a larger moment of inertial will have more total kinetic energy if they rotate and move with the same speed. In other words, if both objects have the same total kinetic energy, the one with a larger moment of inertial has to rotate and move slower (and reach the bottom later). For cylinder and sphere, if they have the same mass and radius, cylinder has a larger moment of inertia because it is more massive at places away from the center. The sphere will have a greater speed and it will reach the bottom first, because its moment of inertia is smaller.

Since both objects have the same mass, the cylinder has less translational kinetic energy because it is moving slower. As we have already discussed, both objects have the same total kinetic energy (=translational kinetic energy + rotational kinetic energy). The cylinder should have more rotational kinetic energy, because its translational kinetic energy is less.