$($a$)$ What is the formula for calculating the pressure due to the height of

liquid?

$($b$)$ Name two devices which make use of this formula when used for

pressure measurement.

$($c$)($i$)$ In the situation shown in Figure $2,$ calculate the pressure

difference between points $1$ and $2$ for the flow of a gas within the

pipe. The liquid present is mercury whose density is

$13560kg{m}^{-3}.$

$($ii$)$ The liquid is now replaced by a new liquid whose density is

$2200kg{m}^{-3}.$ If the pressure difference remains constant, what

will be the new difference in level between each limb$?$

$($iii$)$ What is the advantage of changing the liquid?