The axle of a pulley of mass 1 kg is attached to the end of an elastic string of length 1 m, cross-sectional area ${10}^{-3}{m}^2$  and Young’s modulus $2\times {10}^5\text{}N{m}^{-2}$ , whose other end is fixed to the ceiling. A rope of negligible mass is placed on the pulley such that its left end is fixed to the ground and its right end is hanging freely, from the pulley which is at rest in equilibrium. Now, the free end A of the rope is subjected to pulling with constant force F = 10 N. Friction between the rope and the pulley can be neglected. (Given , $g=10m{s}^{-2}$ )