$A$ beaker of radius $15\, cm$ is filled with a liquid of surface tension $0.075\, N/m$. The force across an imaginary diameter on the surface of the liquid is:

Soap solution is used for cleaning dirty clothes because

Small liquid drops assume a spherical shape because

$A$ thin metal disc of radius $r$ floats on the water surface and bends the surface downwards along the perimeter,making an angle $\theta$ with the vertical edge of the disc. If the disc displaces a weight of water $W$ and the surface tension of water is $T$,then the weight of the metal disc is:

Surface tension is exhibited by liquids due to the force of attraction between the molecules of the liquid. The surface tension decreases with an increase in temperature and vanishes at the boiling point. Given that the latent heat of vaporization for water $L_v = 540 \text{ kcal/kg}$,the mechanical equivalent of heat $J = 4.2 \text{ J/cal}$,density of water $\rho_w = 10^3 \text{ kg/m}^3$,Avogadro's number $N_A = 6.0 \times 10^{26} \text{ molecules/kmol}$,and the molecular weight of water $M_A = 18 \text{ kg/kmol}$.
$(a)$ Estimate the energy required for one molecule of water to evaporate.
$(b)$ Show that the intermolecular distance for water is $d = \left( \frac{M_A}{N_A \rho_w} \right)^{1/3}$ and find its value.
$(c)$ $1 \text{ g}$ of water in the vapour state at $1 \text{ atm}$ occupies $1601 \text{ cm}^3$. Estimate the intermolecular distance at the boiling point in the vapour state.
$(d)$ During vaporisation,a molecule overcomes a force $F$,assumed constant,to go from an intermolecular distance $d$ to $d'$. Estimate the value of $F$.
$(e)$ Calculate $\frac{F}{d}$,which is a measure of the surface tension.

$A$ square frame of each side $L$ is dipped in a soap solution and taken out. The force acting on the film formed is ($T =$ surface tension of soap solution). (in $TL$)