Question

A cylindrical vessel containing a liquid is closed by a smooth piston of mass $m$ as shown in the figure. The area of cross-section of the piston is $A$. If the atmospheric pressure is $P_o$, find the pressure of the liquid just below the piston.

• A. $P=\frac{P_o}{A}+mg$
• B. $P=\frac{P_o}{A}-mg$
• C. $P=P_o+\frac{mg}{A}$
• D. $P=P_o-\frac{mg}{A}$

Answer 1

The correct option is C $P=P_o+\frac{mg}{A}$

Let the pressure of the liquid just below the piston be $P$. The forces acting on the piston are
(a) its weight, $mg$ (downward)
(b) force due to the air above it, $P_{o}A$ (downward)
(c) force due to the liquid below it, $PA$ (upward)
If the piston is in equilibrium,
$PA=P_{o}A+mg$
or, $P=P_o+\frac{mg}{A}$