Two discs cone of density 7200 `kg//m^(3)` and another of density `9000km//m^(3)` have the same mass and thickness. What is the ratio of their moments of inertia?

Options

A. `(4)/(5)`
B. `(5)/(4)`
C. `(5)/(9)`
D. `(1)/(9xx7.2)`

Answer

B

Explanation

`because " "M_(1)=M_(2)`
`therefore" "v_(1)rho_(1)=v_(2)rho_(2)`
`therefore" "piR_(1)^(2)h rho_(1)=piR_(2)^(2)hrho_(2)`
`therefore" "(R_(1)^(2))/(R_(2)^(2))=(rho_(2))/(rho_(1))" ….(1)"`
`therefore" "(l_(1))/(l_(2))=((1)/(2)MR_(1)^(2))/((1)/(2)MR_(2)^(2))=(R_(1)^(2))/(R_(2)^(2))=(rho_(2))/(rho_(1))`
`=(9000)/(7200)=(5)/(4)`