A soap bubble is being blown on a tube of radius $1 \mathrm{cm}.$ The surface tension of the soap solution is $0.05{\mathrm{Nm}}^{-1}$ and the bubble makes $60°$ with the tube as shown in the figure. Find the excess of pressure over the atmosphere pressure in the tube (in $\mathrm{Pa}$ )

A soap film is made by dropping a circular frame of radius $b$ in soap solution. A bubble is formed by blowing air with speed $v$ in the form of a cylinder. Air stops after striking surface of soap bubble. Density of air is $\rho$. The radius of the bubble is $R>b$. The radius $R$ of the bubble when the soap bubble separates from the ring is $\frac{\beta T}{\rho v^2}.$ Find the value of $\beta .$ (where, surface tension of liquid is $T$ ).

A circular ring has inner and outer radii equal to $20 \mathrm{mm}$ and $50 \mathrm{mm}$ respectively. Mass of the ring is $m=0.8 \mathrm{g}$. It gently pulled out vertically from a water surface by a sensitive spring. When the spring is stretched $4 \mathrm{cm}$ from its equilibrium position the ring is on verge of being pulled out from the water surface. If spring constant is $k=0.9 \mathrm{N} {\mathrm{m}}^{-1}$ and $g=10 \mathrm{m} {\mathrm{s}}^{-2}$, the surface tension of water(in $\mathrm{N} {\mathrm{m}}^{-1}$) is $x\times {10}^{-3}$. Write the value of $\left[x\right],$ where $\left[ \right]$ is the greatest integer function.

A long thin walled capillary tube of mass $M=10 \mathrm{g}$ and radius $r=7 \mathrm{mm}$ is partially immersed in a liquid of surface tension $T=0.75 \mathrm{N} {\mathrm{m}}^{-1}$. The angle of contact for the liquid and the tube wall is $60°$. How much force(in $\mathrm{N}$) is needed to hold the tube vertically? Neglect buoyancy force on the tube.

(Take $g=10 \mathrm{m} {\mathrm{s}}^{-2}$, $\pi =\frac{22}{7}$)