Two solid sphere (`A` and `B`) are made of metals of different densities `rho_A` and `rho_B` respectively. If their masses are equal, the ratio of their moments of inertia `(I_A/I_B)` about their respective diameter is

Options

A. `((rho_(B))/(rho_(A)))`
B. `((rho_(A))/(rho_(B)))^(2//3)`
C. `(rhoA)/(rhoB)`
D. `(rhoB)/(rhoA)`

Answer

B

Explanation

`m_(A)=m_(B)`
`rArr ((4)/(3)pi R_(A)^(3))rho_(A) = ((4)/(3)pi R_(B)^(3))rho_(B)`
`rArr (R_(A)^(2))/(R_(B)^(2))=((rho_(B))/(rho_(A)))^(2//3)`
Moment of inertia,
`I = (2)/(5)MR^(2) rArr I prop R^(2)`
`rArr therefore (I_(B))/(I_(A))=(R_(B)^(2))/(R_(A)^(2))=((rho_(A))/(rho_(B)))^(2//3)`