Two discs one of density 7.2 g/`cm^(3)` and the other of density 8.9 g/`cm^(3)` are of same mass and thickness. Their moments of inertia are in the ratio

Options

A. `8.9 : 7.2`
B. `7.2 : 8.9`
C. `(8.9 xx 7.2) : 1`
D. `1 : (8.9 xx 7.2)`

Answer

A

Explanation

`(I_(1))/(I_(2)) = ((1)/(2) M_(1) r_(1)^(2))/((1)/(2) M_(2 r_(2)^(2))) = (r_(1)^(2))/(r_(2)^(2))`
As masses of two discs are equal , hence `(pi r_(1)^(2) t) rho_(1) = (pi r_(2)^(2) t) rho_(2)`
or `(r_(1)^(2))/(r_(2)^(2)) = (rho_(2))/(rho_(1)) therefore (I_(1))/(I_(2)) = (rho_(2))/(rho_(1)) = (8.9)/(7.2)`