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Q.

Two liquids of densities $ρ_{1}$ and $ρ_{2} (ρ_{2} = 2 ρ_{1})$ are filled up behind a square wall of side 10 m as shown in figure. Each liquid has a height of 5 m. The ratio of the forces due to these liquids exerted on upper part MN to that at the lower part NO is (Assume that the liquids are not mixing):

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a

1/4

b

1/3

c

2/3

d

1/2

answer is A.

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Detailed Solution

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Force on upper half = $P_{a v g} A$ $= \frac{P_{1} + P_{2}}{2} A = \frac{0 + ρ g 5}{2} A = \frac{ρ g 5}{2} A$
Force on lower half = $P_{a v g} A$ $= \frac{P_{2} + P_{3}}{2} A = \frac{(ρ g 5) + (ρ g 5 + 2 ρ g 5)}{2} A = 2 ρ g 5 A$
$\begin{array}{l} ∴ \frac{F_{U}}{F_{L}} = \frac{ρ g 5 A}{2 (2 ρ g 5) A} = \frac{1}{4} \end{array}$

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