Question

A barometer kept in an elevator reads $76\text{cm}$ of mercury when the elevator is at rest. If the elevator goes upwards with some acceleration, the reading of the barometer will be

• A. $76\text{cm}$
• B. $>76\text{cm}$
• C. $<76\text{cm}$
• D. zero

Answer 1

The correct option is C $<76\text{cm}$

When elevator goes upwards with some acceleration, the effective value of acceleration due to gravity increases due to pseudo force acting downwards.
$\Rightarrow g^{\prime }=g+a...\left(i\right)$
When elevator is at rest, the atmospheric pressure measured by the barometer is,
$P_0=\rho gh...\left(ii\right)$,
where $\rho \to$ density of mercury used in barometer and $h=76\text{cm}$

When the barometer is kept in an elevator moving upwards with acceleration $a$, the atmospheric pressure measured by it will be,
$P_0=\rho g^{\prime }{h}^{\prime }$
$\Rightarrow h^{\prime }=\frac{P_0}{\rho g^{\prime }}...\left(iii\right)$
From Eq.$\left(i\right)\left(ii\right)\&\left(iii\right)$,
$\Rightarrow h^{\prime }=\frac{\rho gh}{\rho (g+a)}=\frac{gh}{g+a}$
Since $(g+a)>g$, $h^{\prime }<h$
$\therefore$ Reading of barometer will be less than $76\text{cm}$