Question

A barometer kept in an elevator reads \[76cm\] when it is at rest if the elevator goes up with increasing speed.

Answer 1

Hint: A barometer is used to calculate the air pressure in a certain environment. When a body is moving upward the acceleration due to gravity is the summation of acceleration of that body with acceleration due to gravity. And then at the second step calculate the pressure of the barometer.

Formula used:
 ${{P}_{0}}={{h}_{0}}\rho (g+a)$
Where:
${{P}_{0}}$ = initial pressure
${{h}_{0}}$ = initial height
$\rho $ = density of mercury

Complete step-by-step answer:
 When the elevator is at rest,
\[{{\rho }_{Hg}}g(\dfrac{76}{100})={{P}_{0}}\Rightarrow \dfrac{76}{100}=\dfrac{{{P}_{0}}}{g{{\rho }_{Hg}}}\]
 (ii) When the elevator is speeding (let the acceleration be a). Then,
​\[{{\rho }_{Hg}}(g+a){{h}_{1}}={{P}_{0}}\]
${{h}_{1}}=\dfrac{{{P}_{0}}}{\left( g+a \right){{\rho }_{Hg}}}$
As \[a>0\],
\[\begin{align}
& {{h}_{1}}<\dfrac{{{P}_{o}}}{g{{\rho }_{Hg}}} \\
& \Rightarrow {{h}_{1}}<h \\
& \Rightarrow {{h}_{1}}<\dfrac{76}{{{w}_{o}}}m \\
\end{align}\]
So, the new reading will be less than $76cm$.

Additional Information: Barometers and pressure altimeters are the same kind of instruments but used for different purposes. An altimeter is used to match different levels of corresponding atmospheric pressure to the altitude, while a barometer is measured subtle pressure changes due to weather pr elements of weather by keeping at the same level. The average atmospheric pressure on the earth’s surface varies between $940hPa\left( mbar \right)$ and $1040hpa\left( mbar \right)$. The average atmospheric pressure at sea level is $101hPa\left( mbar \right)$ . Atmospheric pressure is an indicator of the weather. Changes within the atmosphere, including changes in atmospheric pressure, affect the weather. Meteorologists use barometers to predict short-term changes within the weather.


Note: As in this the elevator going up in direction so, that we have to calculate the acceleration of the elevator according to the sign convention and then use this to calculate the pressure variation of the barometer reading. You should use proper sign convention to calculate the pressure reading accurately so that there will be no mistakes or errors occur.