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

Options

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

Answer

D

Explanation

Here `I_(1)=(1)/(2)mr_(1)^(2)andI_(2)=(1)/(2)mr_(2)^(2)`
`therefore (I_(1))/(I_(2))=(r_(1)^(2))/(r_(2)^(2))` Also if `.rho.` is the thickness
`pir_(1)^(2)rho_(1)=pir_(2)^(2)rho_(2)` (masses equal)
`therefore (r_(1)^(2))/(r_(2)^(2))=(rho_(2))/(rho_(1))=(I_(1))/(I_(1))=(rho_(2))/(rho_(1))`