Question

Length of glass tube in simple barometer is
(A) $100mm$
(B) $1cm$
(C) $100cm$
(D) $1mm$

Answer 1

Hint: Barometer is an instrument which is used to measure the pressure of the atmosphere. It works by balancing the weight of mercury against the pressure in the atmosphere. We can use the simple barometer construction to know the correct answer.

Complete step by step solution:
Let us see the process of how to measure pressure using a mercury barometer.
Barometer works on the principle that we can measure the atmospheric pressure at any point as the weight of the unit cross-sectional area air column which is extended from the point to the top of the atmosphere. The mercury level in the column will rise and fall depending upon the weight of mercury. If the weight comes out to be more than the pressure, then there is a rise in mercury but if the case is reversed then the level of mercury will fall. It was invented in 1643 by Torricelli.
A long glass tube whose one end is open and is about $100cm$ , is filled with mercury. It is then inverted in a dish filled with mercury such that the open end is in the dish. The space above the column of mercury is filled with mercury vapor. The pressure due to this can be neglected as at ordinary temperature, the pressure of these vapors is very small. So, when they are at the same level, the pressure inside the column will be equal to the atmospheric pressure. The atmospheric pressure P in terms of height of column of mercury, can be represented as $P = \rho gh$ where $\rho $ is the density and h is the column of mercury height and g is the acceleration due to gravity.

Hence, the correct option is C.

Note: The mercury column height is independent of the cross-sectional area of the tube but depends upon the mercury density which varies with temperature and the value of acceleration due to gravity which depends on the position.