Question

A solid cylinder with a radius of 4.0 cm has the same mass as a solid sphere of radius R. If the cylinder and sphere have the same moment of inertia about their centers, what is the sphere's radius?

Answer 1

Let

Mass of the cylinder = Mass of the sphere = m

Radius of the cylinder, r = 4 cm

Radius of the sphere, R = ?

Moment of inertia of solid sphere = Moment of inertia of solid cylinder

(2/5) m R^2 = (1/2) m r^2

0.4 R^2 = 0.5 * 4^2

Radius of the sphere, R = 4.47 cm

Answer 2

The moment of inertia of solid cylinder is equal to the moment of inertia of solid sphere. 2 2 二(1.11)R, -(1.11) (4 cm) 4.47 cm Therefore, the radius of the sphere is 4.47 cm