Question

The pressure at the bottom of a tank of water is $3P$ where $P$ is the atmospheric pressure. If the water is drawn out till the level of water is lowered by one fifth, the pressure at the bottom of the tank will now be:

• A. $2P$
• B. $\left(13/5\right)P$
• C. $\left(8/5\right)P$
• D. $\left(4/5\right)P$

Answer 1

The correct option is B $\left(13/5\right)P$

If we ignore the atmospheric pressure, the pressure at the bottom is $2P$

We know that the pressure by a liquid column is given by $h\rho g$

$\therefore h\rho g=2P$

After the height getting lowered by one fifth, the height becomes four fifth.

$\therefore \frac{4}{5}h\rho g=\frac{2\times 4}{5}P=\frac{8}{5}P$

Now including the atmospheric pressure it becomes

$(\frac{8}{5}+1)P=\frac{13}{5}P$