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?

From the adjacent figure,the correct observation is:

When an airplane flies at a higher altitude,it is not advisable to keep a fountain pen in one's pocket. Why?

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:

$A$ manometer reads the pressure of a gas in an enclosure as shown in Figure $(a)$. When a pump removes some of the gas,the manometer reads as in Figure $(b)$. The liquid used in the manometers is mercury and the atmospheric pressure is $76 \; cm$ of mercury.
$(a)$ Give the absolute and gauge pressure of the gas in the enclosure for cases $(a)$ and $(b)$,in units of $cm$ of mercury.
$(b)$ How would the levels change in case $(b)$ if $13.6 \; cm$ of water (immiscible with mercury) are poured into the right limb of the manometer? (Ignore the small change in the volume of the gas).

Explain why water storage dam walls are thicker at the bottom.