The height of a mercury barometer is $75 \ cm$ at sea level and $50 \ cm$ at the top of a hill. The ratio of the density of mercury to that of air is $10^4$. The height of the hill is ....... $km$.

The height to which a cylindrical vessel must be filled with a homogeneous liquid,such that the average force with which the liquid presses the side of the vessel is equal to the force exerted by the liquid on the bottom of the vessel,is equal to:

$A$ barometer tube,containing mercury,is lowered in a vessel containing mercury until only $50 \, cm$ of the tube is above the level of mercury in the vessel. If the atmospheric pressure is $75 \, cm$ of mercury,what is the pressure at the top of the tube?

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 $g = 10 \; m \; s^{-2}$)

$A$ $U$-shaped tube is partially filled with an incompressible liquid of density $1.2 \ g \ cm^{-3}$. Oil, which does not mix with the liquid, is poured into the left side of the $U$-tube until the liquid rises by $15 \ cm$ on the right side. If the density of the oil is $0.9 \ g \ cm^{-3}$, the oil level will stand higher than the liquid level on the right side of the $U$-tube by: (in $cm$)

An inverted tube barometer is kept on a lift moving downward with a deceleration $\alpha$. The density of mercury is $\rho$ and the acceleration due to gravity is $g$. If the atmospheric pressure is $P_0$,then: