The figure shows a siphon. Choose the wrong statement: ($P_0 =$ atmospheric pressure)

Who devised for the first time,a method for measuring atmospheric pressure?

$A$ 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?

$(a)$ 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.

$A$ swimming pool has a depth of $3 \,m$. The pressure at the bottom of the pool due to water alone is: (Density of water is $1000 \,kg \,m^{-3}$, Acceleration due to gravity $= 10 \,m \,s^{-2}$)

As the depth increases in a vessel filled with liquid, the pressure ..........