Question

Pressure exerted by a liquid at a given point is
A.directly proportional to the depth of the point in the liquid
B.directly proportional to the density of liquid
C.both (a) and (b)
D.none of these

Answer 1

We can understand that liquid applies the same amount of pressure in every direction of its container, free from the shape of the container. Because we know that any liquid applies pressure at a point that is determined by the density of the liquid and the vertical depth. Hence the pressure applied by a liquid is not dependent on the area of cross-section.

Complete answer:
Let us consider the depth at which pressure is applied is $h$
It is already known that any liquid applies pressure at a point that is dependent on the density of the liquid and the vertical depth.
If we take the liquid has a density $\rho$
the depth is given $= {\text{ }}h$
And, the acceleration due to gravity is $g$.
The pressure applied by liquid at depth is
$P{\text{ }} = {\text{ }}h\rho g$
here,$\;P$ is the pressure applied by liquid
Therefore pressure applied by liquid $= h\rho g$

Hence Option C is correct.

Note:
This equation has common validity past the special conditions below which it is derived here. Even if the container was absent, the surrounding fluid would still apply this pressure, making the fluid static. Therefore the equation $P{\text{ }} = {\text{ }}h\rho g$ signifies the pressure caused by the weight of any fluid of average density $\rho$ at any depth $h$ underneath its surface. In almost incompressible liquids, this equation holds to great depths. In rather compressible gases, we can apply this relation given that the density variations are small over the depth considered.