Two identical cylindrical vessels with their bases at the same level each contain a liquid of density . The height of liquid in one vessel in and that in the other is . The area of either base is . What is the work done by gravity in equalizing the levels when the vessels are interconnected?
Step 1: Write the given data.
Two identical cylindrical vessels with density .
= The height of liquid in one vessel.
= The height of the other vessel.
= Area of the base.
Step 2: Write the work done formula.
Where,
= Mass of the liquid.
= Height of the liquid.
Step 3: To find the height of the liquid.
Let us assume that the height is
is the area of cross-section.
Height of the liquid is given by:
Hence decrease in height in vessel of height is given by,
Step 4: Find the mass of the mass of the liquid.
Mass of liquid would be equal to
Substitute in the above formula,
Step 5: Solve for work done.
= Mass of the liquid.
= Height of the liquid.
Replace the above data in the work done formula,
Therefore the work done by gravity in equalizing the levels when the vessels are interconnected is .