Horizontal plate of area 0.036 m2 is beneath the surface of liquid of density 930 kg m–3. Force on the plate due to the pressure of liquid is 290 N. What is the depth of plate beneath the surface of the liquid?

Question:

                Horizontal plate of area 0.036 m² is beneath the surface of liquid of density 930 kg m^–3. Force on the plate due to the pressure of liquid is 290 N.
What is the depth of plate beneath the surface of the liquid?
A 0.88 m                     B 1.13 m                     C 8.7 m                       D 9.1 m

Solution:

Answer: A.

Pressure P = hρg

where h is the depth, ρ is the density of the liquid and g is the acceleration of free fall.

But,

Pressure P = Force / Area = F / A

Therefore,

Depth h = P / ρg = F / (Aρg) = 290 / [0.036 (930) (9.81)] = 0.88m