Question

A mercury barometer reads $ 75\;cm\; $ in a stationary lift. What reading does it show when the lift is moving downwards, with an acceleration of $ 1\;m{s^{ - 2}} $ ?

Answer 1

Hint: A barometer is a measuring instrument which measures the atmospheric pressure which is called barometric pressure. Mercury barometer helps us to determine the atmospheric pressure by measuring the movement of mercury in a glass tube. So with the help of the mercury, we can find out the pressure reading in the mercury barometer in the given case.

Complete answer:
We know that a barometer is a measuring instrument which measures the atmospheric pressure which is called barometric pressure. So, when we use a mercury barometer, we determine the atmospheric pressure by measuring the movement of mercury in a glass tube.
The formula used to measure barometric pressure in atm is:
 $ {P_{atm}} = \rho hg $
Where, $ \rho $ is density of mercury, g is known as gravitational acceleration, and h is the height of mercury column above the free surface area.
Now, we are given acceleration, a is $ 1\;m{s^{ - 2}} $ which is in downward direction because lift is moving downward.
Therefore, the net acceleration will be $ {a_n}_ = (g - a)\; $
Therefore, the formula becomes:
 $ \rho gh\prime = \rho (g - a)h\; $
Where h’ is the final height of the barometer.
Therefore, on cancelling density (rho) on both sides, the equation becomes:
 $ h\prime = h(1 - a/g)\;\_\_\_\_(1) $
Now, the values given are:
 $ a = 1\;m{s^{ - 2}} $
 $ g = 1\;0m{s^{ - 2}} $
 $ h = 75cm $
Put these values in first equation and we get:
 $ h' = 75\left( {1 - \dfrac{1}{{10}}} \right) $
On simplifying, we get
 $ h' = 75\left( {\dfrac{9}{{10}}} \right) $
 $ h' = 67.5cm $
Hence, the reading shown by the barometer when the lift is moving downwards, with an acceleration of $ 1\;m{s^{ - 2}} $ is $ 67.5cm $ .

Note :
We should keep in mind that, while equating the two equations of pressure, that is one for the initial pressure and other one is for the pressure when lift is moving in downward direction, the units should be same of each element in the equation, and here the density of the mercury plays an important role in determining the atmospheric pressure with the help of mercury barometer.