One end of a nylon rope of length 1 and diameter 10 mm is fixed to free limb. A monkey weighing 100 N jumps to catch the free end and stays there. The change in diameter of the rope is (Young's modulus of the wire is Y and Poisson Ratio is )

Step-by-step solution

The Young modulus Y is defined as the ratio of longitudinal stress to longitudinal strain. The longitudinal stress is _ stress = F A = F r^2 = F (d/2)^2 = 4F d^2 , where F = 100 N and d = 10 mm = 0.01 m. The longitudinal strain is _L = l l = _ stress Y = 4F d^2 Y . The Poisson ratio is defined as the ratio of lateral strain to longitudinal strain: = - _D _L , where _D = d d is the lateral strain. Therefore, the change in diameter d is given by d = - _L d = - ( 4F d^2 Y ) d = - 4F d Y . Substituting the given values