A narrow, uniform glass tube, closed at one end, constains air which is sealed by a thread of mercury. The…

Analyze the question: A glass tube closed at one end traps air behind a thread of mercury. We compare the trapped air when the tube lies horizontally with when it stands vertically with the open end up.

Concept: The pressure of the trapped air depends on the position of the tube. Boyle's law applies at constant temperature: P₁L₁ = P₂L₂, because the tube is uniform and the volume is proportional to the length.

Solution:

1. Horizontal position: The mercury thread's weight acts along the tube, not on the air. So the trapped air pressure equals atmospheric pressure: P₁ = H (atmospheric pressure)

2. Vertical position, open end up: The mercury sits on top of the air, so its weight adds pressure: P₂ = H + h, where h is the length of the mercury thread (in cmHg)

3. Apply Boyle's law: H × L₁ = (H + h) × L₂ L₂ = L₁ × H / (H + h)

Since (H + h) > H, we get L₂ < L₁.

So the air column is shorter in the vertical position than in the horizontal position.

Check the options:

• A: Wrong. It says the opposite.
• B: Correct. The air length in the vertical position is less than in the horizontal position.
• C and D: Wrong. The mercury thread's length stays the same, because the tube is uniform and mercury is practically incompressible.
• E: Wrong. The air pressure is atmospheric only in the horizontal position. In the vertical position it is atmospheric pressure plus the mercury pressure.

Tip: With the open end up, the mercury pushes down on the air and compresses it, so the air column is shorter. With the open end down, the air pressure is H − h, so the air expands and the column is longer. In the horizontal position the air pressure is simply atmospheric.