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 P₀, find the pressure of the liquid just below the piston.

• A.
• B.
• C.
• D. P₀

Answer 1

The correct option is B

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,$P_0$ A (downward)

(c) force due to the liquid below it, PA (upward)

If the piston is in equilibrium,

$PA=P_{0}A+mg$

or,P=$P_0+\frac{mg}{A}$