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


A
P=PoA+mg
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B
P=PoAmg
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C
P=Po+mgA
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D
P=PomgA
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Solution

The correct option is C P=Po+mgA
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, PoA (downward)
(c) force due to the liquid below it, PA (upward)
If the piston is in equilibrium,
PA=PoA+mg
or, P=Po+mgA

Physics

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