Which of the following has the highest moment of inertia when each of them has the same mass and the same radius ?

Options

A. A ring about any of its diameter.
B. A disc about any of its diameter.
C. A hollow sphere about any of its diameter.
D. A solid sphere about any of its diameter.

Answer

C

Explanation

Let M and R be the mass and radius respectively. Moment of inertia of a ring about any of its diameter is
`I_("ring") = 1/2MR^(2)`
Moment of inertia of a hollow sphere about any of its diameter is
`I_("hollow sphere") = 2/5 MR^(2)`
Moment of inertia of a solid sphere and about any of its diameter is
`I_("solid sphere") = 2/5 MR^(2)`
Thus, `I_("hollow sphere")` is largest.