Question

One end of a nylon rope of length $4.5m$ and diameter $6mm$ is fixed to a stem of a tree. A monkey weighting $100N$ jumps to catch the free end and stays there. what will be the change in the diameter of the rope. (Given Young's modulus of nylon $=4.8\times {10}^{11}N{m}^{-2}$ and Poisson's ratio of nylon $=0.2$)

• A. $8.8\times {10}^{-9}m$
• B. $7.4\times {10}^{-9}m$
• C. $6.4\times {10}^{-8}m$
• D. $5.6\times {10}^{-9}m$

Answer 1

Answer: (A)

$8.8\times {10}^{-9}m$

Poisson's ratio $\sigma =\frac{\Delta D/D}{\Delta l/l}=\frac{\Delta D}{D}.\frac{l}{\Delta l}$
$\therefore \Delta D=\frac{\sigma D\Delta l}{l}=\frac{0.2\times 6\times {10}^{-3}\times 3.32\times {10}^{-5}m}{4.5}=8.8\times {10}^{-9}m$