Question

Figure shows a container filled with a liquid of density $\rho$. Four points $A,B,C$ and $D$ lies on the vertices of a vertical square. Points $A$ and $C$ lies on a vertical line and points $B$ and $D$ lies on a horizontal line. Choose the correct statement(s) about the pressure at the four points.

• A. $P_D=P_B$
• B. $P_A<P_B=P_D<P_C$
• C. $P_D=P_B=\frac{P_C-P_A}{2}$
• D. $P_D=P_B=\frac{P_C+P_A}{2}$

Answer 1

Answer: (A), (B), (D)

The correct options are
A $P_D=P_B$
B $P_A<P_B=P_D<P_C$
D $P_D=P_B=\frac{P_C+P_A}{2}$

According to Pascal's law,
$P_D=P_B$ , because $B$ and $D$ lie on the same horizontal plane.


Let $l$ be the side of the square. Then the vertical distance between $A$ and $C$ is $l\sqrt{2}$.
$P_D=P_B=P_C-\rho g\frac{l}{\sqrt{2}}--\left(i\right)$
Similarly, $P_D=P_B=P_A+\rho g\frac{l}{\sqrt{2}}--\left(ii\right)From\left(i\right)and\left(ii\right),P_B=P_D=\frac{P_A+P_C}{2}$