Two cylindrical vessels of equal cross-sectional area 16 cm² contain water upto heights 100 cm and 150 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 and g = 10 ms^–2]

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0.25 J

1 J

8 J

12 J

answer is B.

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Detailed Solution

$h = \frac{h_{1} + h_{2}}{2}$

Now,

$\begin{array}{l} W = U_{i} - U_{f} \\ W = ({ρAh}_{1}) g \frac{h_{1}}{2} + (ρ {Ah}_{2}) g \frac{h_{2}}{2} - ρA (h_{1} + h_{2}) g (\frac{h_{1} + h_{2}}{4}) \\ \begin{array}{l} W = \frac{ρAg}{2} [h_{1}^{2} + h_{2}^{2} - \frac{{(h_{1} + h_{2})}^{2}}{2}] \\ W = 1 J \end{array} \end{array}$