Question

Explain how is the height of mercury column in tube of a simple barometer is a measure of the atmospheric pressure.

Answer 1

A mercury barometer consists of a column of mercury suspended with its open end in a basin of mercury.
The pressure at a depth in a liquid is given by $P_0+\rho gh$ where $P_0$ is the pressure at the surface, $\rho$ is the density of the liquid, and $h$ is the depth from the surface of the water.
Above the mercury column is vacuum, hence $P_0=0$ The pressure at the point where the column meets the surface will be $P=\rho gh$.
Since fluids have a property that points at the same level in the same fluid have the same pressure, we get the relation that atmospheric pressure acting in the surface of mercury in the basin = $\rho gh$