Question

If the value of ‘g’ at a place is decreased by $2\%$ . The barometric height of the mercury
A.Increases by $2\%$
B.Decreases by $2\%$
C.Remains unchanged
D.Sometimes increases and sometimes decreases

Answer 1

A barometer is used to measure atmospheric pressure. Torricelli invented Barometers. It was found that the rise in the height of the level depends on the density of liquid used, atmospheric pressure, and acceleration due to gravity. And we know acceleration due to gravity changes when we move in the depth of the earth or too high from the earth’s surface.

Complete answer:
It is given that the value acceleration due to gravity decreased by $2\%$.
We have to calculate the change in the barometric height of the mercury.
The relation between the barometric height of mercury and acceleration due to gravity is given by the following formula.
$h = \dfrac{P}{{\rho g}}$
Here $h$is the barometer height of mercury, $P$is pressure, $\rho$is the density, and $g$is the acceleration due to gravity.
Now here $P,\rho$ are constant.
So height is inversely proportional to the acceleration due to gravity.
$h \propto \dfrac{1}{g}$
Hence, if the acceleration due to gravity will decrease by $2\%$ then the barometric height of mercury will increase by $2\%$.

Hence, the correct option is (A) increased by $2\%$.

Note:
One atmospheric pressure is defined when the height of mercury in the barometer rises to $76cm$
One Torricelli is the pressure when the mercury rises to $1mm$ .
Due to changes in weather conditions, to calculate scientific data $1$ atmospheric pressure and zero degree Celsius is used.
The height of mercury in a barometer decreases if a drop of water is added inside the barometer.