Two cylindrical vessels of equal cross sectional area of \(2 \mathrm{~m}^2\) contain water up to height 10 m and 6 m , respectively. If the vessels are connected at their bottom then the work done by the force of gravity is : (Density of water is \(10^3 \mathrm{~kg} / \mathrm{m}^3\) and \(\mathrm{g}=10 \mathrm{~m} / \mathrm{s}^2\))

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(D) \(8 \times 10^4 \mathrm{~J}\)

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\(\begin{aligned} & \mathrm{U}_1=(\rho \mathrm{A} \times 10) \mathrm{g} \times 5+(\rho \mathrm{A} 6) \mathrm{g} \times 3 \\ & \mathrm{U}_{\mathrm{i}}=\rho \mathrm{Ag}(50+18) \\ & \mathrm{U}_{\mathrm{i}}=68 \rho \mathrm{Ag}\end{aligned}\)
\(\begin{aligned} & U_f=(\rho A \times 16) g \times 4 \\ & =(\rho A g) \times 64\end{aligned}\)
\(\begin{aligned} & \omega=\Delta U=4 \times \rho A g \\ & =4 \times 1000 \times 2 \times 10=8 \times 10^4 \mathrm{~J}\end{aligned}\)

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