$A$ barometer tube reads $75 \,cm$ of $Hg$. If the tube is gradually inclined at an angle of $30^{\circ}$ with the horizontal,keeping the open end in the mercury container,then find the length of the mercury column in the barometer tube in $cm$.

The atmospheric pressure at a place is $10^5 \,Pa$. If tribromomethane (specific gravity $= 2.9$) is employed as the barometric liquid,the barometric height is .......... $m$. (in $.52$)

Describe the mercury barometer for the measurement of atmospheric pressure.

$(a)$ Pressure decreases as one ascends the atmosphere. If the density of air is $\rho$,what is the change in pressure $dp$ over differential height $dh$?
$(b)$ Considering the pressure $P$ to be proportional to the density,find the pressure $P$ at a height $h$ if the pressure on the surface of the earth is $P_{0}$.
$(c)$ If $P_{0} = 1.03 \times 10^5 \text{ N/m}^2$,$\rho_0 = 1.29 \text{ kg/m}^3$,and $g = 9.8 \text{ m/s}^2$,at what height will the pressure drop to $\frac{1}{10}$ of the value at the surface of the earth?
$(d)$ This model of the atmosphere works for relatively small distances. Identify the underlying assumption that limits the model.

$A$ bubble of volume $V_0$ is released from a depth $h$ in a lake. If the atmospheric pressure is $P$ and the temperature is assumed to be constant,what is the new volume of the bubble when it reaches the surface? (Density of water is $\rho$)

Explain how an open-ended tube manometer measures pressure.