A solid sphere, a solid cylinder, a spherical shell, and a hoop all have the same mass and radius. Each are rolling on a horizontal surface with the same center of mass speed, and then they roll up identical inclines. Which one goes the greatest distance up its incline?
A) the hoop
B) the solid sphere
C) the spherical shell
D) the cylinder
E) They all go the same distance up their inclines.

Question

Quizplus · Accepted Answer

According to the principle of conservation of energy, the object that reaches the highest height up the incline will be the one that has the greatest amount of potential energy. The potential energy of a rolling object depends on its moment of inertia (I). The moment of inertia of each object is given by:

Solid sphere: I = (2/5) * MR^2
Solid cylinder: I = (1/2) * MR^2
Spherical shell: I = (2/3) * MR^2
Hoop: I = MR^2

Since all the objects have the same mass and radius, the hoop has the smallest moment of inertia and hence the greatest potential energy at the top of the incline. Therefore, the hoop will go the greatest distance up its incline.

A Solid Sphere, a Solid Cylinder, a Spherical Shell, and a Hoop