If `I_(1),I_(2)` and `I_(3)` are the moments of inertia about the natural axies of solid sphere, hollow sphere and a spherical shell of same mass and radii, the correct result of the following is

Options

A. `I _(1) gt I _(2) gt I _(3)`
B. `I _(3) gt I _(2) gt I _(1)`
C. `I _(2) gt I _(1) gt I _(3)`
D. `I _(2) gt I _(3) gt I _(1)`

Answer

B

Explanation

Let m be the mass and r be the radius of the bodies, then the moment of inertia of solid sphere will be,
`I _(1) = (2)/(5) mr ^(2)`
The moment of inertia of hollow sphere will be,
`I _(2) = (2)/(3) mr ^(2)`
The moment of inertia of the ring is given by,
`I _(3) = mr ^(2)`
Therefore, `I _(3) gt I _(2) gt I _(1).`