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?

Solution:

Radius of solid cylinder = 4.0 cm = 0.04 m

Formula for moment of inertia of a cylinder is

I(C) = 1/2 mr²

Where I is the moment of inertia

m is the mass of cylinder

r is the radius of cylinder

The formula for moment of inertia of a sphere is

I(C) = 2/5 MR²

According to the question I(C) = I(S)

1/2 mr² = 2/5 MR²

As m = M

1/2 r² = 2/5 R²

It can be written as

1/2 × 5/2 × r² = R²

5/4 r² = R²

5/4 × 0.04² = R²

R² = 5/4 × 0.0016 = 0.002

So we get,

R = 0.0447 m

R = 4.47 cm

Therefore, the radius of the sphere is 4.47 cm.

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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?

Summary:

If 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, then the sphere’s radius is 4.47 cm.