$A$ sudden drop in the mercury level by $10 \,mm$ or more is a sign of ..........

The heights of mercury in a barometer at the base and at the top of a mountain are $75 \, cm$ and $50 \, cm$,respectively. If the ratio of the density of mercury to the density of air is $10^4$,what is the height of the mountain?

What are the difficulties arising from using water in a barometer instead of mercury?

In a cylindrical container open to the atmosphere from the top,a liquid is filled up to a $10\, m$ depth. The density of the liquid varies with depth $h$ from the surface as $\rho(h) = 100 + 6h^2$,where $h$ is in meters and $\rho$ is in $kg/m^3$. The pressure at the bottom of the container will be: (Atmospheric pressure $P_0 = 10^5\, Pa$,$g = 10\, m/s^2$)

The pressure acting on a submarine is $3 \times 10^{5} \; Pa$ at a certain depth. If the depth is doubled,the percentage increase in the pressure acting on the submarine would be: (Assume that atmospheric pressure is $1 \times 10^{5} \; Pa$,density of water is $10^{3} \; kg \; m^{-3}$,and $g = 10 \; m \; s^{-2}$)

The density of the atmosphere is $1.29 \ kg/m^3$. If the atmospheric pressure is $1.013 \times 10^5 \ Pa$,how high would the atmosphere extend if the density were uniform? $(g = 9.81 \ m/s^2)$