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QJEEM22Ph51aa: JEE Main 2022 Physics - Class 11 JEEM22Ph51aa Solution: Two cylindrical vessels of equal cross-sectional area contain…

Two cylindrical vessels of equal cross-sectional area 16 cm216 \mathrm{~cm}^{2} contain water upto heights 100 cm100 \mathrm{~cm} and 150 cm150 \mathrm{~cm} respectively. The vessels are interconnected so that the water levels in them become equal. The work done by the force of gravity during the process, is [Take, density of water =103 kg/m3=10^{3} \mathrm{~kg} / \mathrm{m}^{3} and g=10 ms−2\mathrm{g}=10 \mathrm{~ms}^{-2} ] :

Multiple Choice Options

  • A 0.25 J
  • B 1 J
  • C 8 J
  • D 12 J

Step-by-Step Verified Solution

A=16×10−4A = 16 \times {10^{ - 4}} m2

JEE Main 2022 (Online) 27th July Morning Shift Physics - Properties of Matter Question 123 English Explanation

Ein=m1gH12+m2gH22{E_{in}} = {m_1}g{{{H_1}} \over 2} + {m_2}g{{{H_2}} \over 2}

=ρgA2(H12+H22)=ρgA2(12+1.52)= \rho g{A \over 2}\left( {H_1^2 + H_2^2} \right) = \rho g{A \over 2}\left( {{1^2} + {{1.5}^2}} \right)

Efin=ρgA2(2H2)=ρgA2(2×1.252){E_{fin}} = \rho g{A \over 2}\left( {2{H^2}} \right) = \rho g{A \over 2}\left( {2 \times {{1.25}^2}} \right)

W=ρgA2(3.25−3.125)W = \rho g{A \over 2}\left( {3.25 - 3.125} \right)

=1= 1 J

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