## Question

Two identical cylindrical vessels, each of base area *A*, have their bases at the same horizontal level. They contain a liquid of density . In one vessel the height of the liquid is *h*_{1} and in the other *h*_{2} > *h*_{1}. When the two vessels are connected, the work done by gravity in equalizing the levels is

### Solution

After the levels in the two vessels becomes equal, the increase in height of the liquid in one vessel is with the same decrease in height in the other. Thus, effectively a slab of liquid in thickness falls a vertical distance equal to its thickness under the action of gravity.

Therefore,

Work done by the gravity is

Where mass of slab *m* is given by

Therefore,

.

#### SIMILAR QUESTIONS

The dimensions of viscosity in terms of M, L and T are

The dimensions of Reynold’s number are

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