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?

The radius of the sphere is 4.47 cm

Explanation:

Parameter given:

Radius of cylinder, R = 4.0cm = 0.04m

The formula for moment of inertia of the cylinder is given as

I (C) = 1/2 * mr²

Where I = moment of inertia

m = mass of cylinder

r = radius of cylinder

The moment of inertia of the sphere is given as:

I (S) = 2/5 * MR²

Where M = mass of sphere

R = radius of sphere.

From the question, I (C) = I (S), hence,

1/2 * mr² = 2/5 * MR²

Since m = M

1/2 * r² = 2/5 * R²

1/2 * 5/2 * r² = R²

5/4 r² = R²

=> 5/4 * 0.04² = R²

=> R² = 5/4 * 0.0016 = 0.002

=> R = 0.0447 m = 4.47 cm

Therefore, radius of the sphere is 4.47 cm