Two circular iron discs are of the same thickness. The diameter of A is twice of B . The moment of inertia of A as compared to that of B is

Options

A. twice as large
B. four as large
C. 8 time as large
D. 16 times as large

Answer

D

Explanation

M.I. of disc `=(1)/(2)mR^(2)=(1)/(2)(pi R^(2)t)rho R^(2)=(1)/(2)pi R^(4)t rho`
[`rho` = density, t = thickness]
If discs are made of same material and same thickness then `I prop R^(4) prop ("Diameter")^(4)`
`therefore (I_(1))/(I_(2))=((D_(A))/(D_(B)))^(4)=((2)/(1))^(4)-(16)/(1)`.