A mercury barometer reads 75 cm. If the tube be inclined by 60^∘ from vertical, the length of m

step 1 Given cushion we are given a mercury barometer and it is given that in vertical condition the me

A mercury barometer reads 75 cm. If the tube be inclined by...

A mercury barometer reads $75 \mathrm{~cm}$. If the tube be inclined by $60^{\circ}$ from vertical, the length of mercury in the tube will be
(A) $37.5 \mathrm{~cm}$
(B) $150 \mathrm{~cm}$
(C) $\frac{75 \sqrt{3}}{2} \mathrm{~cm}$
(D) $100 \mathrm{~cm}$

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Key Concepts

Trigonometric Relationships

Trigonometry, particularly the cosine function, is used here to relate the vertical height of the liquid to its length along an inclined tube. The vertical height equals the product of the inclined column length and the cosine of the inclination angle, allowing the computation of one from the other.

Inclined Column Geometry

When a column of liquid is oriented at an angle rather than vertically, the actual length along the tube is different from the vertical height. It is necessary to understand that while the vertical component remains the same, the path along the tube is longer due to the angle of inclination.

Hydrostatic Equilibrium

This concept deals with the balance between the gravitational force acting on a fluid and the pressure gradient within it. In a barometer, the weight of the mercury column is in equilibrium with the atmospheric pressure, and the height of the column reflects this balance.

Barometric Measurement

Barometric measurement uses the height of a liquid column (typically mercury) in a tube to determine atmospheric pressure. The pressure exerted by the atmospheric air is directly related to the height of the mercury column in the device.

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