Question

An incompressible liquid of density riscontained in a vessel of uniform cross-sectional area A. If the atmo-
spheric pressure is p, then the fore acting on a horizontal plane of area a situated at a depth d in liquid is given
by:
(1) ap+apgh
(2) P÷a +Pgd÷a
(3) p+pgd÷ a
(4) A(Pgd +p)
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Answer 1

Answer:

In an incompressible liquid, Pressure increase with increase in depth. Hence force acting on horizontal plane of area a at depth d is given by,

Force = Pa, where p is pressure acting on horizontal plane and a is area of plane.

Pressure of incompressible liquid P acting along horizontal plane is greater than atmospheric pressure by ρgd ,where ρ is density of given liquid, g is acceleration due to gravity and d is depth.

P=p+ρgd

Hence Force= (p+ρgd)a

Explanation:

the correct option is d