Two cylindrical vessels of equal cross-sectional area 16 cm 2 contain water upto heights 100 cm and 150 cm respectively. The vessels are interconnected so that the water levels in them become equal. T

Question

Two cylindrical vessels of equal cross-sectional area 16 cm 2 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 = 10 3 kg m - 3 and g = 10 ms - 2 ]

TestHub · Accepted Answer

Initially, the centre of mass of the right column will be at height of $75 cm$ and the centre of mass of the left column will be at $50 cm$ . After opening of the valve both columns will have height of $125 cm$ and their centre of mass will be at height $\frac{125}{2} cm$ . Therefore,
$W = - ∆ U = - [(m_{1} + m_{2}) g \frac{h_{1} + h_{2}}{4} - m_{1} g \frac{h_{1}}{2} - m_{2} g \frac{h_{2}}{2}]$
Now, $m_{1} = ρ A h_{1}$ and $m_{2} = ρ A h_{2}$
Putting $ρ = 1000 kg m^{- 3}, g = 10 m s^{- 2}, h_{1} = 100 cm, h_{2} = 150 cm$ and $A = 16 \times 10^{- 4} m^{2}$ , we get,
$W = 1 J$

Physics - Fluid Question with Solution | TestHub

Options:

Doubts & Discussion