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 $P_0 = 10^5\, Pa$,$g = 10\, m/s^2$)

Explain why you cannot make a decent cup of tea on a mountain.

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 ....... $km$.

$A$ 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).

From the adjacent figure,the correct observation is:

The pressure at the bottom of a liquid tank is not proportional to the