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Directions: The following question is based on the paragraph given below.

A fixed, thermally conducting cylinder has a radius R and height L0. The cylinder is open at its bottom, and has a small hole at its top. A piston of mass M is held at a distance L from the top surface, as shown in the figure. The atmospheric pressure is P0. The piston is taken completely out of the cylinder. The hole at the top is sealed. A water tank is brought below the cylinder and put in a position, so that the water surface in the tank is at the same level as the top of the cylinder as shown in the figure. The density of water is ρ. In equilibrium, the height H of water column in the cylinder satisfies: ### Options :-

1. ρg(L0 - H)2 + P0(L0 - H) + L0P0 = 0
2. ρg(L0 - H)2 - P0(L0 - H) - L0P0 = 0
3. ρg (L0 - H)2 + P0(L0 - H) - L0P0 = 0
4. ρg (L0 - H)2 - P0(L0 - H) + L0P0 = 0
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