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. $\frac{13}{5}P$
• C. $\frac{8}{5}P$
• D. $\frac{4}{5}P$

Answer 1

The correct option is B $\frac{13}{5}P$

Let $h$ be the initial height of water and $h_1$ be the height of water level when decreased by one-fifth.
$\therefore h_1=h-\frac{h}{5}=\frac{4}{5}h$
Initially, $3P=P+\rho gh$
$\Rightarrow 2P=\rho gh$
Finally,
$P^{\prime }=P+\rho g\left(\frac{4}{5}h\right)=P+\frac{4}{5}\times 2P=\frac{13}{5}P$