Question

The pressure at the bottom of a water tank is $6P$, where $P$ is the atmospheric pressure. If water is drawn out till the level decreases by $\frac{2}{5}th$, then the pressure at the bottom of the tank is

• A. $2P$
• B. $4P$
• C. $6P$
• D. $5P$

Answer 1

The correct option is B $4P$

Let the height of the water in the tank is $h$.
Difference in pressure, $6P-P={\rho }_{w}gh$
Where, ${\rho }_w$ is density of water
$5P={\rho }_{w}gh...\left(1\right)$
$\because {\frac{2}{5}}^{th}$ of water taken out from the tank. So, ${\frac{3}{5}}^{th}$ of water is left to exert the pressure.
Let $P^{\prime }$ be the pressure exerted by the ${\frac{3}{5}}^{th}$ of water at the bottom of a water tank.
So, $P^{\prime }=P+\frac{3}{5}{\rho }_{w}gh$
$P^{\prime }=P+\frac{3}{5}\times 5P$ [from equation $\left(1\right)$]
$\Rightarrow P^{\prime }=4P$
$\therefore$ Pressure at the bottom of the tank is $4P$.