Two discs have same mass and thickness. Their materials are of densities `pi_(1)` and `pi_(2)`. The ratio of their moment of inertia about central axis will be

Options

A. `1:rho_(1)rho_(2)`
B. `rho_(1)rho_(2):1`
C. `rho_(1):rho_(2)`
D. `rho_(2):rho_(1)`

Answer

D

Explanation

Moment of inertia of disc, `I=(1)/(2)MR^(2)=(1)/(2)M((M)/(pi rhot))`
`(because rho=(M)/(V)=(M)/(piR^(2)t):. R^(2)=(M)/(pi rhot))`
`I = (1)/(2) (M^(2))/(pi rho t)`
`:. I prop (1)/(rho)` (As M and t are constant)
`(I_(1))/(I_(2))=(rho_(2))/(rho_(1))`.