Two soap bubbles of radius 2 cm and 4 cm , respectively, are in contact with each other. The radius of curvature of the common surface, in cm , is _________.

Two persons pull a wire towards themselves. Each person exerts a force of $$200 \mathrm{~N}$$ on the wire. Young's modulus of the material of wire is $$1 \times 10^{11} \mathrm{~N} \mathrm{~m}^{-2}$$. Original length of the wire is $$2 \mathrm{~m}$$ and the area of cross section is $$2 \mathrm{~cm}^2$$. The wire will extend in length by _________ $$\mu \mathrm{m}$$.

Small water droplets of radius $$0.01 \mathrm{~mm}$$ are formed in the upper atmosphere and falling with a terminal velocity of $$10 \mathrm{~cm} / \mathrm{s}$$. Due to condensation, if 8 such droplets are coalesced and formed a larger drop, the new terminal velocity will be ________ $$\mathrm{cm} / \mathrm{s}$$.

A liquid column of height $$0.04 \mathrm{~cm}$$ balances excess pressure of a soap bubble of certain radius. If density of liquid is $$8 \times 10^3 \mathrm{~kg} \mathrm{~m}^{-3}$$ and surface tension of soap solution is $$0.28 \mathrm{~Nm}^{-1}$$, then diameter of the soap bubble is __________ $$\mathrm{cm}$$. (if $$\mathrm{g}=10 \mathrm{~m} \mathrm{~s}^{-2}$$ )