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 to lower the level of water by one fifth then, the pressure at the bottom of the tank will be

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

Answer 1

Answer: (B)

$\left(13/5\right)P$

Let h be the initial height of water and $h_1$ be the height of water level decreases by one fifth.
$h_1=h-\frac{1}{5}h=\frac{4}{5}h$
Initially, $3P=P+\rho gh$
$\Rightarrow 2P=\rho gh$
Finally,
$P^{{}^{\prime }}=P+\frac{4}{5}\rho gh=P+\frac{4}{5}\times 2P=\frac{13}{5}P$