A container is entirely filled with water, and the pressure at the bottom of the

Question

A container is entirely filled with water, and the pressure at the bottom of the container is P. Then the container is emptied halfway and topped off with oil of density 0.80 x 103 kg/m3 which floats on top of the water. What is the ratio of the pressure P' at the bottom of the container now with respect to the pressure when only water was present in the container? (the density of water is (1 x 103 kg/m3). Neglect air pressure when answering the problem (i.e. we are comparing gauge pressures).

Answers:

A) P'/P = 1.1

B) P'/P = 0.9

C) The pressure does not change.

D) I am unable to determine this with the given information.

Explanation / Answer

Let the depth of container = h
Pressure in case of water = density of water * acceleration due to gravity * depth
P = 1*10^3 * g *h
P = 1000gh

Pressure in case of oil + water = density of water * acceleration due to gravity * depth + density of oil * acceleration due to gravity * depth
P1 =  1*10^3 * g *h/2 + 0.8 * 10^3 * g*h/2
P1 = 900gh

Ratio of the pressure P' at the bottom of the container now with respect to the pressure when only water was present in the container =
P' = P1/P
P' = 900gh/1000gh
P' = 0.9

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