If `rho` is density of the material of a sphere of radius R . Then its moment of inertia about its diameter is

Options

A. `(8pi)/(15)rhoR^(5)`
B. `(4pi)/(3)rhoR^(5)`
C. `(2pi)/(5)rhoR^(5)`
D. `(4pi)/(3)rhoR^(4)`

Answer

A

Explanation

`I=(2)/(5)MR^(2)=(2)/(5)rho vR^(2)`
`=(2)/(5)rho (4pi)/(3)R^(3)R^(2)`
`= (8pi)/(15)rho R^(5)`.