Explanation:
Work done by gravity is given by the formula,
W = [tex]\rho A (h_{1} - h)g (h - h_{2})[/tex] ......... (1)
It is known that when levels are same then height of the liquid is as follows.
h = [tex]\frac{h_{1} + h_{2}}{2}[/tex] ......... (2)
Putting value of equation (2) in equation (1) the overall formula will be as follows.
W = [tex]\frac{1}{4} \rho gA(h_{1} - h_{2})^{2})[/tex]
= [tex]\frac{1}{4} \times 1.23 g/cm^{3} \times 9.80 m/s^{2} \times 3.89 \times 10^{-4} m^{2}(1.76 m - 0.993 m)^{2})[/tex]
= 0.689 J
Thus, we can conclude that the work done by the gravitational force in equalizing the levels when the two vessels are connected is 0.689 J.
