Rotating spheres of variable densities!

The densities of two solid spheres AA and BB of the same radius RR vary with radial distance rr as

ρA(r)=k(rR)andρB(r)=k(rR)5,\rho_A (r) = k \left( \dfrac rR \right) \quad \text{and} \quad \rho_B (r) = k {\left( \dfrac rR \right)}^5,

respectively, where kk is a constant.

Let the moments of inertia of the individual spheres about the axes passing through their centers be IAI_A and IBI_B, respectively.

If  IBIA=n10\ \dfrac{I_B}{I_A} = \dfrac{n}{10}, then find the value of nn.


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