A solid sphere of radius R, a solid cylinder of radius R, and a hollow cylinder

Question

A solid sphere of radius R, a solid cylinder of radius R, and a hollow cylinder of radius R all have the same mass, and all three are rotating with the same angular velocity. The sphere is rotating around an axis through its center, and each cylinder is rotating around its symmetry axis. Which one has the greatest rotational kinetic energy?

both cylinders have the same rotational kinetic energy

the solid cylinder

the solid sphere

they all have the same rotational kinetic energy

the hollow cylinder

Explanation / Answer

for hollow cylinder I =MR2

for solid cylinder I. =1/2(MR)

for sphere I=2/5(MR2)

rotational k.e. directly proportional to I

hence hollow cylinder has highest k.e.

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