If the radius of a sphere is doubled by keeping its mass constant, compare the moment of inertia of the old…

Moment of inertia of the sphere $I=\frac{2m{r}^2}{5}$

Moment of inertia of the old sphere  $I_{\mathrm{old}}=\frac{2m{r}^2}{5}$

Moment of inertia of the old sphere $I_{\mathrm{new}}=\frac{2m{\left(2r\right)}^2}{5}$

Ratio of moment of inertia of the old sphere to new sphere

$\frac{I_{\mathrm{old}}}{I_{\mathrm{new}}}=\frac{\frac{2m{\left(r\right)}^2}{5}}{\frac{2m{\left(2r\right)}^2}{5}}=\frac{1}{4}$