Two identical cylindrical vessel with their bases at the same level each contain a liquid of density `rho`. The height of the liquid in one vessel is `h_(1)` and in the other is `h_(2)` the area of either base is A. What is the work done by gravity is equalising the levels when the two vessels are connected?

Explanation

To find the work done by gravity in equalizing the levels of the liquid in two identical cylindrical vessels when they are connected, we can follow these steps:

### Step 1: Understand the Initial Conditions
We have two identical cylindrical vessels with:
- Density of the liquid: \( \rho \)
- Height of the liquid in the first vessel: \( h_1 \)
- Height of the liquid in the second vessel: \( h_2 \)
- Area of the base of each vessel: \( A \)
...