Question

The figure shows a container filled with a liquid of density $\rho$. Four points $A,B,C$ and $D$ lie on the vertices of a vertical square. Points $A$ and $C$ lie 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 $P_D=P_B=\frac{P_C+P_A}{2}$


Lets say that depth of $A,B,C,D$ are $h_A,h_B,h_C,h_D$, and $P_o$ be atmospheric pressure.
$P_A=P_o+\rho g{h}_A$
$P_B=P_o+\rho g{h}_B$
$P_C=P_o+\rho g{h}_C$
$P_D=P_o+\rho g{h}_D$
As $h_B=h_D\Rightarrow P_B=P_D$,
As $h_A<h_B=h_C<h_D\Rightarrow P_A<P_B=P_C<P_D$
Since ABCD is a square, we can have that
$h_B=h_D=\frac{h_C+h_A}{2}$
$\rho g{h}_B=\rho g{h}_D=\rho g\frac{(h_C+h_A)}{2}$
$P_B-P_o=P_D-P_o=\frac{(P_A-P_o+P_C-P_o)}{2}$
$P_B=P_D=\frac{(P_A+P_C)}{2}$