Question

Two cylindrical vessels of equal cross-sectional area 11.5cm2 are joined together and partially filled with mercury. In one of the vessels, a litre of water is poured on top of the mercury and a body weighing 150 g-wt is allowed to float on the water. What will be the change in the level of the mercury in the other vessel after addition of the water and the floating body?

Answer 1

Answer: A ≅ 3.7cm.

Explanation:

After the addition of the water, the level of the mercury in the first vessel decreases by a height h, and in the second it increases by the same value.

The pressure resulting from the difference in the height of the mercury 2h will be counterbalanced by the weight of the column of water P and the weight of the floating body p. That is, at equilibrium we have

2dgh = (P + p)/*,

where d is the density of mercury. Thus h = (P + p)/2gdh.