Question

A barometer kept in an elevator reads $76cm$ when the elevator is accelerating upwards. The most likely pressure inside the elevator (in $cmofHg$) is

Answer 1

Step 1: Given Data

Let the height of this mercuric column be $h=76cm$.

Let the density of mercury be $\rho$.

Let the acceleration due to gravity be $g$.

Let the acceleration of the lift be $a$.

Step 2: Atmospheric Pressure

A barometer is a tube that is dipped in mercury.

Due to the external atmospheric pressure, the mercuric column rises inside the tube to a certain height.

The atmospheric pressure can be given as

$p_A=h\rho g$

Step 3: Pressure inside the elevator

If the lift uniformly accelerates in the upward direction, the effective value of $g$ can be given as,

$g_{eff}=g+a$

Therefore, the effective pressure inside the lift can be given as

$p_{eff}=h\rho \left(g+a\right)$

Since the $g_{eff}>g$, in order to keep the effective pressure constant, the value of $h$ must decrease.

But it is given that the value of $h$ remains constant.

Therefore, the value of effective pressure must increase.

$\therefore p_{eff}>p_A$

$\Rightarrow p_{eff}>76cmofHg$

Hence, the pressure inside the elevator must be greater than $76cmofHg$.