Three liquids have same surface tension and densities $$\rho_1, \rho_2$$, and $$\rho_3\left(\rho_1>\rho_2>\rho_3\right)$$. In three identical capillaries rise of liquid is same. The corresponding angles of contact $$\theta_1, \theta_2$$ and $$\theta_3$$ are related as

The height of liquid column raised in a capillary tube of certain radius when dipped in liquid '$$A$$' vertically is $$5 \mathrm{~cm}$$. If the tube is dipped in a similar manner in another liquid '$$B$$' of surface tension and density double the values of liquid '$$A$$', the height of liquid column raised in liquid '$$B$$' would be (Assume angle of contact same)

A film of soap solution is formed between two straight parallel wires of length $$10 \mathrm{~cm}$$ each separated by $$0.5 \mathrm{~cm}$$. If their separation is increased by $$1 \mathrm{~mm}$$ while still maintaining their parallelism. How much work will have to be done?

(surface tension of solution $$=65 \times 10^{-2} \mathrm{~N} / \mathrm{m}$$ )

A soap bubble of radius '$$R$$' is blown. After heating a solution, a second bubble of radius '$$2 \mathrm{R}$$' is blown. The work required to blow the $$2^{\text {nd }}$$ bubble in comparison to that required for the $$1^{\text {st }}$$ bubble is