Two discs have same mass and thickness. Their materials are of densities `d_(1) and d_(2)`. The ratio of their moments of inertia about an axis passing through the centre and perpendicular to the plane is

Options

A. `d_(1) : d_(2)`
B. `d_(2):d_(1)`
C. `((d_(1))/(d_(2)))^(2)`
D. `((d_(2))/(d_(1)))^(2)`

Answer

B

Explanation

We have, `(piR^(2)td)=m" "(because "mass = density" xx "volume")`
`R^(2)=(m)/(pid)`
Now, `I=(1)/(2)mR^(2)=(m^(2))/(2pitd)or I prop (1)/(d)`
`:.` The ratio of moments of inertia, `(I_(1))/(I_(2))=(d_(2))/(d_(1))`.