If the pressure at half the depth of a lake is equal to $2/3$ of the pressure at the bottom of the lake,then what is the depth of the lake in $m$? (Assume atmospheric pressure $P_0 = 10^5 \ Pa$,density of water $\rho = 10^3 \ kg/m^3$,and $g = 10 \ m/s^2$)

$A$ barometer tube reads $76 \ cm$ of mercury. If the tube is gradually inclined at an angle of $60^\circ$ with the vertical,keeping the open end immersed in the mercury reservoir,the length of the mercury column will be ........ $cm$.

$A$ submarine has a window of area $30 \times 30 \,cm^2$ on its ceiling and is at a depth of $100 \,m$ below sea level. If the pressure inside the submarine is maintained at the sea-level atmospheric pressure,then the force acting on the window is ............. $N$ (consider density of sea water $\rho = 1.03 \times 10^3 \,kg/m^3$,acceleration due to gravity $g = 10 \,m/s^2$).

The pressure at the bottom of a water tank is $4 P$,where $P$ is atmospheric pressure. If water is drawn out until the water level decreases by $\frac{3}{5}$ of its initial height,then the pressure at the bottom of the tank is .........

$A$ tank is filled with a liquid of density $\rho$ up to a height $H$. The average pressure on the walls of the container is:

Describe the Torricelli experiment for the measurement of atmospheric pressure.