A wire of length L and radius a rigidlyl fixed at one end. On stretching the other end of the wire with a force F, the increase in its length is L, if another wire of same material but of length 2 L and radius 2 a is stretched with a force 2 F, the increase in its length will be

Explanation

In first case , ` Y = (f//pi r^2)/(l//L) = (fL)/(pi r^2 l) ….. (i)`
in second case, let x be the extension in the wire of radius 2r , length 2 L under a load 2 f, then `Y = (2f//pi(2r)^2)/(x//2L) = (fL)/(pi r^2 x) ….. (ii)`
Since Y is same for two cases as the two wires are of same meterial, hence form (i) and (ii) `(fL)/(pi r^2 l) = (fL)/(pi r^2x) or x =l`