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Question
A simple U tube contains mercury to the same level in both of its arms. If water is poured to a height of 13.6 cm in one arm, how much will be the rise in mercury level in the other arm?
Given : density of mercury = 13.6 x 103 kg m-3 and density of water = 103 kg m-3.
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Solution
Given, ρm = 13.6 × 103 kg m -3, ρw = 103 kg m -3
Height to which water is poured in one arm, hw = 13.6 cm
By pouring 13.6 cm of water, the mercury level in the left arm goes down to point A by x cm, while in the right arm, it rises to point C by x cm. Therefore, BC = hm = 2x cm
By Pascal's law,
Pressure in the water column = pressure in the mercury column
Therefore, PA = PB
⇒ hw ρw g = hm ρm g
⇒ 13.6 × 103 × g = 2𝑥 × 13.6 × 103 × g
⇒ 1 = 2𝑥
⇒ 𝑥 = `1/2` = 0.5 cm
Hence, the rise in mercury level = 0.5 cm
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