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

( c) Let `M` and `R` be the mass and radius respectivley. Moment of interia of a ring about any its diameter is
`I_(ring) = (1)/(2) MR^2`
Moment of interia of a disc about any of its diameter is
`I_(disc) = (1)/(4) MR^2`
Moment of interia of a hollow sphere about any of its diameter is
`I_(hollow sphere) = (2)/(3) MR^2`
Moment of interial of a solid sphere about any of its diameter is
`I_(solid sphere) = (2)/(5) MR^2`
Thus, `I_(hollow sphere)` is largest.