What is the moment of inertia of solid sphere of density `rho` and radius `R` about its diameter ?

Options

A. `(105)/(176)R^(2)rho`
B. `(105)/(176)R^(2)rho`
C. `(176)/(105)R^(2)rho`
D. `(186)/(105)R^(2)rho`

Answer

C

Explanation

`I=(2)/(5)MR^(2)=(2)/(5)[(4)/(3)piR^(2)rho]R^(2)=(8)/(15)piR^(5)rho`
`I=(176)/(105)R^(5)rho" "(because pi=(22)/(7))`