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A column of mercury of 10 cm length is contained in the middle of a narrow horizontal 1 m long tube which is closed at both the ends. Both the halves of the tube contain air at a pressure of 76 cm of mercury. By what distance will the column of mercury be displaced if the tube is held vertically?

A column of mercury of 10 cm length is contained in the middle of a narrow horizontal 1 m long tube which is closed at both the ends. Both the halves of the tube contain air at a pressure of 76 cm of mercury. By what distance will the column of mercury be displaced if the tube is held vertically?

Grade:upto college level

1 Answers

Navjyot Kalra
askIITians Faculty 654 Points
6 years ago
M is the mid-point of tube AB.
At equilibrium
p1 x A + mg = p2 x A
p1 x A + 10 x A x dHg = p2 x A
⇒ p1 + 10dHg x g = p2
232-2144_1.jpg
For air present in column AP
p x 45 x A = p1 x (45 + x ) x A
⇒ p1 = 45 / 45 + x x 76 dHg x g …..(ii)
For air present in column QB
p x 45 x A = p2 x (45 – x ) x A
⇒ p2 = 45 / 45 - x x 76 dHg x g (iii)
From (i), (ii) and (iii)
45 x 76 x dHgg / 45 + x + 10 dHg x g = 45 / 45 – x x 76 x dHg x g
⇒ 45 x 76 / 45 + x + 10 = 45 x 76 / 45 – x
x = 2.95 cm.

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