A barometer kept in a stationary elevator reads 76 cm. If the elevator starts accelerating up the reading will be

The correct answer is Less than 76 cm.

Let us understand this step-by-step using the principles of fluid pressure and effective gravity in accelerating frames of reference:

1. Barometer Reading in a Stationary Elevator:
A barometer measures atmospheric pressure by balancing the pressure against the weight of a column of mercury. The relationship between the atmospheric pressure $P$, the density of the mercury $\rho$, the acceleration due to gravity $g$, and the height of the mercury column $h$ is given by:
$P=\rho gh$
When the elevator is stationary, the height of the mercury column is $h=76\text{cm}$.

2. Effect of Upward Acceleration:
When the elevator accelerates upwards with an acceleration $a$, any object inside the elevator experiences an additional downward pseudo-force. This increases the effective acceleration due to gravity $g_{\text{eff}}$ acting on the mercury column, which is now given by:
$g_{\text{eff}}=g+a$

3. Calculating the New Height of the Mercury Column:
The atmospheric pressure $P$ acting on the reservoir of the barometer remains constant. With the increased effective gravity, the pressure balance equation for the new height $h^{\prime }$ becomes:
$P=\rho (g+a)h^{\prime }$
Rearranging the formula to solve for the new height $h^{\prime }$:
$h^{\prime }=\frac{P}{\rho (g+a)}$

Since the denominator has increased because $g+a>g$, the height of the mercury column must decrease:
$h^{\prime }<h$
Therefore, the barometer reading will be less than 76 cm.