Two liquids of densities ρ₁ and ρ₂ ( ρ₂ = 2 ρ₁) are filled up behind… | JEE Main 2020 (8 Jan, Shift 2)

Q19JEE Main 2020 · 8 JAN · SHIFT 2Difficult

Pressure in a Fluid

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)

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Answer: (c)

Force on a vertical strip = average pressure $\times$ area; both parts have area $5\times10 = 50\text{ m}^2$ .
MN: average pressure $= \rho_1 g\times2.5$ , so $F_1 = 2.5\rho_1 g\times50$ .
NO: average pressure $= \rho_1 g\times5 + \rho_2 g\times2.5 = 5\rho_1 g + 5\rho_1 g = 10\rho_1 g$ , so $F_2 = 10\rho_1 g\times50$ .
$\dfrac{F_1}{F_2} = \dfrac{2.5}{10} = \dfrac{1}{4}$
So the answer is (c) 1/4.

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Pressure in a Fluid question from JEE Main 2020 (8 Jan, Shift 2)

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