A wire of cross-section $$A$$ is stretched horizontally between two clamps located $$2 l$$ metre apart. A weight $$w \mathrm{~kg}$$ is suspended from the mid-point of the wire. If the mid-point sags vertically through a distance $$x<1$$, the strain produced is

The Young's modulus of a rope of $$10 \mathrm{~m}$$ length and having diameter of $$2 \mathrm{~cm}$$ is $$200 \times 10^{11} \mathrm{~dyne} / \mathrm{cm}^2$$. If the elongation produced in the rope is $$1 \mathrm{~cm}$$, the force applied on the rope is