Two disc has same mass rotates about the same axis with their densities `rho_(1)` and `rho_(2)` respectively such that `(rho_(1)gt rho_(2))`, then the relation between `I_(1)` and `I_(2)` will be

Options

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

Answer

A

Explanation

`(I_(1))/(I_(2))=(R_(1)^(2))/(R_(2)^(2))` …….(i)
`M_(1)=M_(2)`
`rho_(1)pi R_(1)^(2)t = rho_(2)pi R_(2)^(2)t`
`(rho_(1))/(rho_(2))=(R_(2)^(2))/(R_(1)^(2))`
`therefore` The equation (i) becomes,
`(I_(1))/(I_(2))=(rho_(2))/(rho_(1)) " as " rho_(1) gt rho_(2)`
`(I_(1))/(I_(2))lt 1`
`therefore I_(1) lt I_(2)`.