Moment of inertia of the earth about an axis passing through its centre of mass is (where R and `rho` are radius and density of the earth respectively).

Options

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

Answer

C

Explanation

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