Umakant Kondapure, Collin Fernandes, Nipun Bhatia, Vikram Bathula and, Ketki Deshpande Solutions for Chapter: Surface Tension, Exercise 3: Competitive Thinking

When one end of the capillary is dipped in water, the height of water column is $h$. The upward force of 105 dyne due to surface tension is balanced by the force due to the weight of water column. The inner circumference of the capillary is (Surface tension of water is $\left.7\times {10}^{-2}\mathrm{N} {\mathrm{m}}^{-1}\right)$

Two soap bubbles $A$ and $B$ Are kept in a closed chamber where the air is maintained at pressure $8 \mathrm{N} {\mathrm{m}}^{-2}$. The radii of bubbles $A$ and $B$ are $2 \mathrm{cm}$ and $4 \mathrm{cm}$ Respectively. The surface tension of the soap-water used to make bubble is $0.04 \mathrm{N} {\mathrm{m}}^{-1}$. Find the ratio $\frac{n_{\mathrm{B}}}{n_{\mathrm{A}}},$ where $n_{\mathrm{A}}$ and $n_{\mathrm{B}}$ Are the number of moles of air in bubbles $A$ and $B$, respectively. [Neglect the effect of gravity.]

A certain number of spherical drops of a liquid of radius $r$ coalesce to form a single drop of radius $R$ and volume $V\mathit{.}$ If $T$ is the surface tension of the liquid, then

Pressure inside two soap bubbles are $1.01$ and $1.02$ $\mathrm{atm}$. Ratio between their volumes is

A glass tube of the uniform internal radius $r$ has a valve separating the two identical ends. Initially, the valve is in a tightly closed position. End $1$ has a hemispherical soap bubble of radius End $2$ has a sub-hemispherical soap bubble as shown in the figure. Just after opening the valve, 

The excess pressure inside the first soap bubble is three times that inside the second bubble. Then the ratio of the volumes of the first and second bubbles is 

A large number of liquid drops each of radius $a$ are merged to form a single spherical drop of radius $b$. The energy released in the process is converted into kinetic energy of the big drop formed. The speed of the big drop is $[\rho$ is density of liquid, $T$ is surface tension of liquid]

A uniform capillary tube of length $l$ and inner radius r with its upper end sealed is submerged vertically into water. The outside pressure is $P_0$ and surface tension of water is $\gamma .$ When a length $x$ of the capillary is submerged into water, it is found that water levels inside and outside the capillary coincide. The value of $x$ is