Surface Tension Questions

Consider a water tank as shown in the figure. It has one wall at $x=L$ and is very wide in the $z$ direction. When filled with a liquid of surface tension $S$ and density $\rho$, the liquid surface makes an angle ${\theta }_0$ (${\theta }_0\ll 1$) with the $x$ -axis at $x=L$. If $y(x)$ is the height of the surface, then the equation for $y(x)$ is:(Take $\theta (x)\approx \sin \theta (x)\approx \tan \theta (x)=\frac{dy}{dx}$ and $g$ as acceleration due to gravity)

A balloon is made of a material of surface tension $S$ and its inflation outlet (from where gas is filled in it) has small area $A$. It is filled with a gas of density $\rho$ and takes a spherical shape of radius $R$. When the gas is allowed to flow freely out of it, its radius $r$ changes from $R$ to $0$ (zero) in time $T$. If the speed $v(r)$ of gas coming out of the balloon depends on $r$ as $r^{\alpha }$ and $T\propto S^a{A}^{\beta }{\rho }^{\gamma }{R}^{\delta }$ then:

The surface tension of which of the following liquid is maximum ?

The wettability of a surface by a liquid depends primarily on:

A certain number of spherical drops of a liquid of radius ‘r’ coalesce to form a single drop of radius ‘R’ and volume ‘V’. If ‘T’ is the surface tension of the liquid, then:

Water rises to a height $h$ in a capillary tube. If the length of capillary tube above the surface of water is made less than $h$, then:

A rectangular film of liquid is extended from $(4\text{cm}\times 2\text{cm})$ to $(5\text{cm}\times 4\text{cm})$. If the work done is $3\times 10^{-4}\text{J}$, the value of the surface tension of the liquid is:

Three liquids of densities ${\rho }_1,{\rho }_2$ and ${\rho }_3$ (with ${\rho }_1>{\rho }_2>{\rho }_3$), having the same value of surface tension $T$, rise to the same height in three identical capillaries. The angles of contact ${\theta }_1,{\theta }_2$ and ${\theta }_3$ obey: