Question

Two solid sphere (`A` and `B`) are made of metals of different densities `rho_A` and `rho_B` respectively. If their masses are equal, the ratio of their moments of inertia `(I_A/I_B)` about their respective diameter is

Answer 1

As two solid spheres are equal in masses, so
`m_(A)=m_(B)implies4/3piR_(A)^(3)rho_(A)=4/3piR_(B)^(3)rho_(B)rArr(R_(A))/(R_(B))=((rho_(B))/(rho_(A)))^(1//3)`
The moment of inertia of sphere about diameter
`I=2/5 mR^(2)rArr(I_(A))/(I_(B))=((R_(A))/(R_(B)))^(2)rArr(I_(A))/(I_(B))=((rho_(B))/(rho_(A)))^(2//3)`