A wire of cross sectional area A, modulus of elasticity $$2 \times 10^{11} \mathrm{~Nm}^{-2}$$ and length $$2 \mathrm{~m}$$ is stretched between two vertical rigid supports. When a mass of $$2 \mathrm{~kg}$$ is suspended at the middle it sags lower from its original position making angle $$\theta=\frac{1}{100}$$ radian on the points of support. The value of A is ________ $$\times 10^{-4} \mathrm{~m}^2$$ (consider $$x<<\mathrm{L}$$ ).

(given : $$\mathrm{g}=10 \mathrm{~m} / \mathrm{s}^2$$)

A big drop is formed by coalescing 1000 small droplets of water. The ratio of surface energy of 1000 droplets to that of energy of big drop is $$\frac{10}{x}$$. The value of $$x$$ is ________.

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, $$\mathrm{g}=10 \mathrm{~m} / \mathrm{s}^2$$).