JEE PYQ: Mechanical Properties Of Fluids Question 20
Question 20 - 2020 (09 Jan 2020 Shift 1)
Two liquids of densities $\rho_1$ and $\rho_2$ ($\rho_2 = 2\rho_1$) 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):
(1) 1/3
(2) 2/3
(3) 1/2
(4) 1/4
Show Answer
Answer: (4) 1/4
Solution
Let $P_1$, $P_2$ and $P_3$ be the pressure at points $M$, $N$ and $O$ respectively. Pressure is given by $P = \rho gh$ $P_1 = 0$ ($\because h = 0$) $P_2 = \rho g(5) = 5\rho g$
$P_3 = \rho g(15) = 15\rho g$
Force on upper part, $F_1 = \frac{(P_1 + P_2)}{2} \cdot A$ Force on lower part, $F_2 = \frac{(P_2 + P_3)}{2} \cdot A$ $\therefore \frac{F_1}{F_2} = \frac{5\rho g}{20\rho g} = \frac{5}{20} = \frac{1}{4}$
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