Question

Question #89cc5

Answer 1

We know that the moment of inertia `I` of a disk is related with its mass `M` and radius `R` as follows

`color(blue)(I=1/2MR^2.......................[1])`

Now `M=4/3piR^3drho`

where `m->"mass" , d->"thickness" and rho ->"density"`

`=>R=((3M)/(4pidrho))^(1/3)`

`=>R^2=((3M)/(4pidrho))^(2/3)`

Hence equation [1] becomes

`color(green)(I=1/2Mxx((3M)/(4pidrho))^(2/3).......................[2])`

Now if `M and d` are remaining constant as per given condition then

`color(red)(Iprop1/rho^(2/3).......................[3])`

If the moment of inertia of first disk of density `rho_1=7.2"g/"cm^3` be `I_1` and the moment of inertia of 2nd disk of density `rho_2=8.9"g/"cm^3` be `I_2` then the ratio of moment of inertia of two disks is given by

`color(blue)(I_1/I_2=(rho_2/rho_1)^(2/3)=(8.9/7.2)^(2/3)~~1.15)`