The value of g at a place decreases by 2%. The barometric height of mercury

The correct option is Increases by 2%.

To understand why, let us analyze the relationship between barometric height and the acceleration due to gravity.
The atmospheric pressure at a place, $P$, is balanced by the pressure exerted by the mercury column in the barometer. The pressure exerted by a fluid column of height $h$ is given by the formula:
$P=\rho ·g·h$
where:
- $P$ is the atmospheric pressure (which remains constant at a given instant and location),
- $\rho$ is the density of mercury,
- $g$ is the acceleration due to gravity, and
- $h$ is the barometric height of the mercury column.

Rearranging the formula to express the barometric height $h$, we get:
$h=\frac{P}{\rho ·g}$

Since the atmospheric pressure $P$ and the density of mercury $\rho$ are constant, we can see that the barometric height is inversely proportional to the acceleration due to gravity:
$h\propto \frac{1}{g}$

When the value of $g$ decreases, the height $h$ must increase to maintain the same pressure balance.
Specifically, if $g$ decreases by 2%, let the new gravity be $g^{\prime }=0.98g$.
The new height $h^{\prime }$ will be:
$h^{\prime }=\frac{P}{\rho ·g^{\prime }}=\frac{P}{\rho ·\left(0.98g\right)}=\frac{h}{0.98}\approx 1.02h$

This indicates that the barometric height increases by approximately 2%.