A light cylindrical tube 'T' of length `l` 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 atmosphere pressure is to be `P_(0)`)
Assume that density of air is very small than density of block and water. Pick up the correct statement (s)

Options

A. the volume of block B is `(pi r^(2) l)/(3)`
B. the volume of block B is `(2 pi r^(2) l)/(3)`
C. the pressure of air trapped in the tube is `P_(1) + d g(h + (l)/(3))`
D. the pressure of air trapped in the tube is `P_(0) + d g (h + (2l)/(3))`

Answer

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
`2d Vg + pi r^(2) (2l)/(3) dg =(V + pi r^(2) l)dg`
where V is the volume of block B
`rArr (2d -d)V = (pi r^(2) l d)/(3)`
or `V = (pi r^(2) l)/(3)`
The pressure of the air trapped inside the tube is same as pressure at point A in the water as shown in figure.

`:. P = P_(0) +(h + (l)/(3))dg`
`P_(a) =P_(0) + dg(h + (l)/(3))`.