Question

A solid sphere of radius 3 cm and mass of 100 g rolls down a 30 degree incline from a height of 1 m. A hoop of the same mass and radius rolls down the same incline from the same height. What is the linear velocity of each body at the bottom of the incline? From what height would the body with the larger moment of inertia have to roll down from so that the two linear velocities at the bottom of the incline would be the same?

Answer 1

Do not forget to include rotational kinetic energy when you apply the law of conservation of energy.

It is very unlikely that a hoop "of the same radius" will have the same mass as the sphere. It also turns out that the mass and radius do not affect the result. The sphere wil travel faster because the coefficient in front of MR^2 in the moment of inertia term is less. The M and R terms cancel out when calculating the speed.

This is another poorly formulated question. You are wasting your time taking this course from such an incompetent instructor or school