Question

A light cylindrical tube T of length and radius r containing air is inverted in water (density $d_1$). One end of the tube is open and the other is closed. A block B of density $d_2$ ( >$d_1$) is kept on the tube as shown in the figure. The tube stays is equilibrium in the position shown. Find the volume of B . The density of the air is negligible as compared with the density of water. What is the pressure of the air in the tube assuming that the atmospheric pressure is $P_0$.

Answer 1

As the complete system is in equation then, the mass of $B$, be $m$.

$\therefore$ $mg=\Pi r^2\frac{l}{3}g$.

$\therefore$ $\frac{m}{d_2}=\frac{{\Pi r}^{2}l}{3d_2}$

$\therefore$ Volume of $B=\frac{{\Pi r}^{2}l}{3d_2}$

And the pressure is, $P=P_0+h{d}_{1}g+\frac{{\Pi r}^{2}lg}{3{\Pi r}^2}$

$=P_0+h{d}_{1}g+\frac{lg}{3}$

${hd}_{1}g$ for the water pressure & $\frac{lg}{3}$ for the pressure of the block.