A hollow spherical shell of outer radius $R$ floats just submerged under the water surface. The inne

Question

A hollow spherical shell of outer radius $R$ floats just submerged under the water surface. The inner radius of the shell is $r$. If the specific gravity of the shell material is $\frac{27}{8}$ with respect to water, the value of $r$ is

Professor PC Thomas Classes · Answer

Weight = Buoyancy $\implies \frac{4}{3}\pi(R^3 - r^3)\rho_s g = \frac{4}{3}\pi R^3 \rho_w g \implies (\frac{R^3-r^3}{R^3}) \frac{27}{8} = 1 \implies r = \frac{8}{9}R$.