Question

A hollow thick spherical shell float on water surface with half its volume immersed in it. If its relative density of material of sphere is 4/7 and outer radius is 'r', the inner radius of the sphere is a) r/4 b) r/3 c) 2r/3 d) r/2

Answer 1

Dear Student,

According to buoyancy force.

weight of sphere= weight of liquid displaced.
$$\begin{gathered} weightofsphere \\ w={\rho }_{sphere}\frac{4}{3}\pi (r^3-{r_1}^3). \\ weightofliquiddisplaced. \\ w={\rho }_{water}\frac{4}{2\times 3}\pi \left(r^3\right). \\ equatingabove2equation. \\ {\rho }_{sphere}\frac{4}{3}\pi (r^3-{r_1}^3).={\rho }_{water}\frac{4}{2\times 3}\pi \left(r^3\right) \\ \frac{4}{7}\frac{4}{3}\pi (r^3-{r_1}^3)=\frac{4}{2\times 3}\pi \left(r^3\right). \\ 8(r^3-{r_1}^3)=7r^3 \\ {r_1}^3=\frac{r^3}{8} \\ therefore, \\ {r}_1=\frac{r}{2}.... \end{gathered}$$
regards