Question

The L-shaped fish tank shown in the figure is filled with water and is open at the top. If $d=5.0\text{m}$, what is the ratio of force exerted by the water on face A and face B? (Take $g=10{\text{m/s}}^2$ and neglect atmospheric pressure)

• A. $4:5$
• B. $5:4$
• C. $3:5$
• D. $5:3$

Answer 1

The correct option is A $4:5$

The force on face A of area $A_A$ due to the water pressure is
$F_A=P_A{A}_A$
$={\rho }_{w}g{h}_A{A}_A$
$={\rho }_{w}g\left(2d\right)(d{)}^2$

The force on face B of area $A_B$ due to water pressure is
$F_B={\rho }_{w}g{h}_{avg}{A}_B$
$={\rho }_{w}g\left(\frac{5d}{2}\right)d^2$

So, $\frac{F_A}{F_B}=\frac{{\rho }_{w}g\left(2d\right)(d{)}^2}{{\rho }_{w}g\left(\frac{5d}{2}\right)(d{)}^2}$
$\Rightarrow \frac{F_A}{F_B}=\frac{4}{5}$
Hence, option (A) is correct.