A sphere of solid material of relative density $9$ has a concentric spherical cavity and floats having just sinked in water. If the radius of the sphere be $R$, then the radius of the cavity $(r)$ will be related to $R$ as :-
Diffcult
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$\frac{4}{3} \pi\left(\mathrm{R}^{3}-\mathrm{r}^{3}\right) \rho \mathrm{g}=\frac{4}{3} \pi \mathrm{R}^{3} \rho_{\mathrm{w}} \mathrm{g}$
$9\left(R^{3}-r^{3}\right)=R^{3}$
$r^{3}=\frac{8 R^{3}}{9}$
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