The mercury column in a simple mercury barometer is of height 5m above the mercury in a reservoir. If the tube…

Analyze the question: A mercury barometer's tube is replaced with a wider one (twice the radius). We need the new height of the mercury column.

Concept: The height of a barometer column depends on atmospheric pressure, not on the tube's cross-sectional area:

P = ρgh, so h = P/(ρg)

Here P is atmospheric pressure, ρ is the density of mercury, and g is gravitational acceleration. None of these depend on the tube's radius.

Why the width doesn't matter:

• A wider tube holds more mercury, so the weight of the column is greater.
• But the area at the base is also greater, so the force is spread over a bigger area.
• Pressure = Weight/Area = (ρ·A·h·g)/A = ρgh. The area cancels.

Solution:

• Original height: h = 5 m
• The atmospheric pressure, mercury density and g are unchanged.
• The new height is therefore h = 5.0 m.

(Note: the real barometer height is about 0.76 m, so "5 m" is just a made-up number for this question, but the principle still holds. Capillary effects are also negligible for these tube widths and are ignored here.)

Answer: B. 5.0 m.

Exam tip: In barometer questions, the height depends only on the liquid's density, g, and atmospheric pressure. Tube width, tube shape, and tilting (the vertical height stays the same) do not change the vertical height. Whenever you see "changing the tube's diameter", think "no change."