Two cylindrical vessels of equal cross-sectional area 16 cm ^ 2...

Initially, the centre of mass of the right column will be at height of $75cm$ and the centre of mass of the left column will be at $50cm$. After opening of the valve both columns will have height of $125cm$ and their centre of mass will be at height $\dfrac{125}{2}cm$. Therefore,

$W = - ∆ U = - \left[\left({m}_{1} + {m}_{2}\right)g\dfrac{{h}_{1} + {h}_{2}}{4} - {m}_{1}g\dfrac{{h}_{1}}{2} - {m}_{2}g\dfrac{{h}_{2}}{2}\right]$

Now, ${m}_{1} = ρA{h}_{1}$ and ${m}_{2} = ρA{h}_{2}$

Putting $ρ = 1000kg{m}^{- 3}, g = 10m{s}^{- 2}, {h}_{1} = 100cm, {h}_{2} = 150cm$ and $A = 16 \times {10}^{- 4}{m}^{2}$, we get,

$W = 1J$