Answer
The height of the tube is 37.5 cm
Work Step by Step
$P = P_0 + \rho~g~h$
where
$P$ is the pressure
$P_0$ is the atmospheric pressure
$\rho$ is the density of the liquid
$h$ is the depth below the surface
We can find the height $h$ of the mercury when the gauge pressure at the bottom of the tube is 50 kPa. Therefore;
$\rho~g~h = 50~kPa$
$h = \frac{50~kPa}{\rho~g}$
$h = \frac{5.0\times 10^4~N/m^2}{(13.6\times 10^3~kg/m^3)(9.80~m/s^2)}$
$h = 0.375~m = 37.5~cm$
The height of the tube is 37.5 cm.
