Question

A light cylindrical tube 'T' of length and radius 'r' containing air is inverted in water (density d). One end of the tube is open and the other is closed. A block 'B' of density 2d is kept on the tube as shown in the figure. The tube stays in equilibrium in the position shown. (Assume the atmospheric pressure is to be P0 .). Assume that density of air is very small than density of block and water. Pick up the correct statement(*).

(A) the volume of block B is πr2l/3

(B) the volume of block B is πr2l/3

(C) the pressure of air trapped in the tube is P0 + d g(h+l/3)

(D) the pressure of air trapped in the tube is P0 + d g (h+2l/3)

Answer 1

Correct option (A,C)

Explanation:

The free body diagram of block + tube inclusive of water is as shown below

Since the block + tube system shown in figure is in equilibrium

∴ Net weight of system = buoyant force

The pressure of the air trapped inside the tube is same as pressure at point A in the water as shown in figure.