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 ]

Step-by-step solution

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 125 2   cm . Therefore, W = - ∆ U = - m 1 + m 2 g h 1 + h 2 4 - m 1 g h 1 2 - m 2 g 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 &