A hydraulic press containing water has two arms with diameters as mentioned in the figure. A force of $$10 \mathrm{~N}$$ is applied on the surface of water in the thinner arm. The force required to be applied on the surface of water in the thicker arm to maintain equilibrium of water is _________ N.

The density and breaking stress of a wire are $$6 \times 10^4 \mathrm{~kg} / \mathrm{m}^3$$ and $$1.2 \times 10^8 \mathrm{~N} / \mathrm{m}^2$$ respectively. The wire is suspended from a rigid support on a planet where acceleration due to gravity is $$\frac{1}{3}^{\text {rd }}$$ of the value on the surface of earth. The maximum length of the wire with breaking is _______ $$\mathrm{m}$$ (take, $$\mathrm{g}=10 \mathrm{~m} / \mathrm{s}^2$$).

Mercury is filled in a tube of radius $$2 \mathrm{~cm}$$ up to a height of $$30 \mathrm{~cm}$$. The force exerted by mercury on the bottom of the tube is _________ N.

(Given, atmospheric pressure $$=10^5 \mathrm{~Nm}^{-2}$$, density of mercury $$=1.36 \times 10^4 \mathrm{~kg} \mathrm{~m}^{-3}, \mathrm{~g}=10 \mathrm{~m} \mathrm{~s}^{-2}, \pi=\frac{22}{7})$$

A soap bubble is blown to a diameter of $$7 \mathrm{~cm}$$. $$36960 \mathrm{~erg}$$ of work is done in blowing it further. If surface tension of soap solution is 40 dyne/$$\mathrm{cm}$$ then the new radius is ________ cm Take $$(\pi=\frac{22}{7})$$.