Two mercury barometers X and Y are set up side by side at the same location. Barometer X has a narrow tube and barometer Y has a wider tube. Both are correc...
Question 1 Report
Two mercury barometers X and Y are set up side by side at the same location. Barometer X has a narrow tube and barometer Y has a wider tube. Both are correctly filled.
Which statement about the mercury column heights h₁ and h₂ is correct?
Answer Details
In a mercury barometer, the height of the mercury column is determined by the balance between atmospheric pressure pushing down on the mercury reservoir and the weight of the mercury column. This gives \(h = \dfrac{P_{\text{atm}}}{\rho g}\).
The tube diameter does not appear in this equation. A wider tube holds more mercury by volume, but the extra weight is spread over a proportionally larger cross-sectional area, so the height remains the same. Both barometers measure the same atmospheric pressure using the same liquid, so \(h_1\) equals \(h_2\).
This is a fundamental property of fluid pressure: it depends on depth (height), density, and gravitational field strength, not on the shape or width of the container.
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