Question

A hollow sphere of external and internal diameter 4cm and 2$cm$ , respectively floats in a liquid of density 3.5$g{cm}^{-3}$ . The level of the liquid coincides with the centre of the sphere. Calculate the density of the material of the sphere.

Answer 1

Weight of floating body$=$weight of liquid displaced

$\rho \frac{4}{3}\pi (4^3-2^3)=1\times \frac{1}{2}\times \frac{4}{3}\pi 4^3\rho =\frac{4\times 4\times 4}{2\times (64\times -8)}\rho =\frac{2\times 4\times 4}{56}=\frac{4}{7}g/{cm}^3=0.571g/{cm}^3$