Between two circular discs of equal mass and equal thickness but of different densities which one would have a greater moment of inertia about its central perpendicular axis?

Explanation

Suppose the mass of each disc is M , thickness d, densities of their materials `rho_(1) and rho_(2)(rho_(1)gtrho_(2))` radii `r_(1)` and `r_(2)` respectively.
`:. " "M = pir_(1)^(2)drho_(1)=pir_(2)^(2)drho_(2)or, r_(1)^(2)rho_(1)= r_(2)^(2)rho_(2)`
or, `(r_(1)^(2))/(r_(2)^(2))=(rho_(2))/(rho_(1))`
`because " "rho_(1)gtrho_(2), (rho_(2))/(rho_(1))lt1 " ":." "(r_(1)^(2))/(r_(2)^(2))lt1`
Moment of inertia of the two discs about their central perpendicular axes are `I_(1)=(1)/(2)Mr_(1)^(2)" ""and"" "I_(2)=(1)/(2)Mr_(2)^(2)`.
`:. " "(I_(1))/(I_(2))=(r_(1)^(2))/(r_(2)^(2))lt1`
`:." "I_(1)ltI_(2)`
So, the disc having a lower density will have a greater moment of inertia about its central perpendicular axis.