Question

A barometer kept in an elevator reads $76\text{cm}$ of $Hg$. If the elevator starts accelerating upwards, then the height of the $Hg$ column in the barometer will be

• A. $76\text{cm}$
• B. less than $76\text{cm}$
• C. greater than $76\text{cm}$
• D. zero

Answer 1

The correct option is B less than $76\text{cm}$

Considering situation when barometer is not kept in elevator.
$\begin{array}{}{P}_{atm}=P_A=P_B=P_C=\rho gh& \text{(1)}\end{array}$
Let's consider the case when barometer is placed in the elevator accelerating upwards with acceleration ${}^{\prime }{a}^{\prime }$.

$\begin{array}{}{P}_B=\rho g_{eff}{h}^{\prime }=\rho (g+a)h^{\prime }& \text{(2)}\end{array}$
Since barometer always reads the atmospheric pressure which remains constant in both cases, height of the mercury column changes.
Thus equating $\left(1\right)$ and $\left(2\right)$,
$\rho gh=\rho (g+a)h^{\prime }$
$\Rightarrow h^{\prime }=h\frac{g}{g+a}$
Since $\frac{g}{g+a}<1$
$\Rightarrow h^{\prime }<h$
Hence height of Hg column will be less than 76 cm when the elevator is accelerating upwards.