Thank you for reporting, we will resolve it shortly
Q.
The ratio of radii of two solid spheres of same material is 1:2. The ratio of moments of inertia of smaller and larger sphers about axes passing through their centers is
Solution:
Let the density of sphere be $\rho$
Now for the bigger sphere let the radius be $2 R$,
$
M _{1}=\frac{4 \pi(2 R )^{3}}{3}
$
Now for smaller sphere let the radius be $R, M_{2}=\frac{4 \pi(R)^{3}}{3}$,
So $M _{1}=8 M _{2}$
Moment of inertia of bigger sphere $I _{1}=\frac{2 M _{1}(2 R )^{2}}{5}$
Moment of inertia of smaller sphere $I _{2}=\frac{2 M _{2}( R )^{2}}{5}$
So $\frac{ I _{2}}{ I _{1}}=1: 32$