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)lt I_(2)`
D. `I_(1)=I_(2)`

Answer

C

Explanation

`I_(1)=(MR_(1)^(2))/(2)` and `I_(2)=(MR_(2)^(2))/(2)`
`(I_(1))/(I_(2))=(R_(1)^(2))/(R_(2)^(2))` and `rho_(1)=(m)/(A_(1))` and `rho_(2)=(m)/(A_(2))`
`(rho_(1))/(rho_(2))=(A_(2))/(A_(1))`
`= (R_(1)^(2))/(R_(1)^(2))`