Two stretched membranes of area 2 cm² and 3 cm² are placed in a liquid at the same depth. The ratio of pressures on them is

The correct option is 1 : 1.

To understand why the ratio of pressures is $1:1$, let us recall the formula for hydrostatic pressure in a fluid at rest.
The pressure $P$ exerted by a liquid of density $\rho$ at a depth $h$ is given by:
$P=P_0+\rho gh$
where:
- $P_0$ is the atmospheric pressure at the surface of the liquid.
- $\rho$ is the density of the liquid.
- $g$ is the acceleration due to gravity.
- $h$ is the depth of the point below the free surface of the liquid.

From this formula, we can see that the hydrostatic pressure at any point inside a liquid depends only on:
1. The depth ($h$) of the point.
2. The density ($\rho$) of the liquid.
3. The acceleration due to gravity ($g$).

Importantly, the pressure does not depend on the surface area of the membrane or object placed in the liquid.
Since both membranes are placed in the same liquid (so density $\rho$ is identical) at the same depth (so depth $h$ is identical), the pressure exerted on both membranes is exactly the same.

Therefore, if $P_1$ is the pressure on the first membrane and $P_2$ is the pressure on the second membrane:
$P_1=P_2$
Thus, the ratio of the pressures is:
$\frac{P_1}{P_2}=\frac{1}{1}$
or $1:1$.