Two circular discs A and B have equal masses and uniform thickness but have densities `rho_(1)` and `rho_(2)` such that `rho_(1)gt rho_(2)` . Their moments of inertia is

Options

A. `I_(1)gt I_(2)`
B. `I_(1)gt gt I_(2)`
C. `I_(1)ltI_(2)`
D. `I_(1)=I_(2)`

Answer

C

Explanation

`(I_(1))/(I_(2))=(M_(1))/(M_(2))xx((R_(1))/(R_(2)))^(2)=((R_(1))/(R_(2)))^(2)`
`M_(1)=M_(2)`
`rho_(1)v_(1)=rho_(2)v_(2)`
`rho_(1)pi R_(1)^(2)t=rho_(2)pi R_(2)^(2)t`
`(rho_(1))/(rho_(2))=((R_(2))/(R_(1)))^(2)`
`therefore (I_(1))/(I_(2))=(rho_(2))/(rho_(1))`
As, `rho_(1) gt rho_(1)`
`(I_(1))/(I_(2)) lt 1`
`I_(1) lt I_(2)`.