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

Options

A. twice as large
B. four times as large
C. sixteen times as large
D. eight times of large

Answer

C

Explanation

`(I_(1))/(I_(2))=(M_(1)R_(1)^(2))/(M_(2)R_(2)^(2))` ……(i)
`M_(1)=rho v_(1)= rho pi R_(1)^(2)t`
`M_(2)= rho v_(2)=rho pi R_(2)^(2) t`
`(M_(1))/(M_(2))=(R_(1)^(2))/(R_(2)^(2))`
Therefore equation nbo. (i) becomes,
`therefore (I_(1))/(I_(2))=((R_(1))/(R_(2)))^(2)xx((R_(1))/(R_(2)))^(2)=((R_(1))/(R_(2)))^(4)`
`(I_(1))/(I_(2))=((2R_(2))/(R_(2)))^(4)=16`