A thin tube sealed at both ends is 100 cm long. It lies horizontally… | JEE Main 2013 (23 Apr, Shift 1)

Q78JEE Main 2013 · 23 APR · SHIFT 1Difficult

Gas Laws & Ideal Gas Equation

A thin tube sealed at both ends is 100 cm long. It lies horizontally, the middle 20 cm containing mercury and two equal ends containing air at standard atmospheric pressure. If the tube is now turned to a vertical position, by what amount will the mercury be displaced?

(Given: cross-section of the tube can be assumed to be uniform)

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Answer: (b)

Each air column is $40$ cm long at $76$ cm of Hg. When vertical, mercury moves down by $x$ : upper column $40 + x$ , lower column $40 - x$ .
Boyle's law: $P_{up} = \frac{76 \times 40}{40 + x}$ , $P_{low} = \frac{76 \times 40}{40 - x}$ .
Equilibrium of mercury: $P_{low} = P_{up} + 20 \Rightarrow 3040\left(\frac{1}{40-x} - \frac{1}{40+x}\right) = 20$
$\Rightarrow x^2 + 304x - 1600 = 0 \Rightarrow x = \frac{-304 + \sqrt{98816}}{2} \approx 5.18$ cm
So the answer is (b) 5.18 cm.

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Gas Laws & Ideal Gas Equation question from JEE Main 2013 (23 Apr, Shift 1)

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