Question

a spherical shell and a solid sphere (both of the same total mass) are rotating about a diameter at the same angular frequency and with the same rotational kinetic energy. what is the ratio of the spherical shell radius to the solid sphere (i.e., rspherical shell/rsolid sphere)?

Answer 1

I (shell) = 2/3 M R^2

I(sphere) = 2/5 M R^2

I(shell) / I(sphere) = (2/3) / (2/5) = 5/3

R(shell) / R(sphere) = (5/3)^1/2 = (15)^1/2 / 3