JEE MAIN - Physics (2022 - 27th July Morning Shift - No. 5)
Two cylindrical vessels of equal cross-sectional area $$16 \mathrm{~cm}^{2}$$ contain water upto heights $$100 \mathrm{~cm}$$ and $$150 \mathrm{~cm}$$ 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 $$=10^{3} \mathrm{~kg} / \mathrm{m}^{3}$$ and $$\mathrm{g}=10 \mathrm{~ms}^{-2}$$ ] :
0.25 J
1 J
8 J
12 J
Explanation
$$A = 16 \times {10^{ - 4}}$$ m2
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$${E_{in}} = {m_1}g{{{H_1}} \over 2} + {m_2}g{{{H_2}} \over 2}$$
$$ = \rho g{A \over 2}\left( {H_1^2 + H_2^2} \right) = \rho g{A \over 2}\left( {{1^2} + {{1.5}^2}} \right)$$
$${E_{fin}} = \rho g{A \over 2}\left( {2{H^2}} \right) = \rho g{A \over 2}\left( {2 \times {{1.25}^2}} \right)$$
$$W = \rho g{A \over 2}\left( {3.25 - 3.125} \right)$$
$$ = 1$$ J
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