Question

One end of a nylon of length $4.5m$ and diameter $6mm$ is fixed to a tree-limb. A monkey weighing $100N$ jumps very slowly to catch the rope and stays there. Find the change in the diameter of the rope. Young’s modulus of nylon $=4.8\times {10}^{11}N{m}^{-2}$ and Poisson’s ratio of nylon $=0.2$.

• A. $4.4\times {10}^{-9}m$
• B. $6.6\times {10}^{-9}m$
• C. $8.8\times {10}^{-9}m$
• D. $2.2\times {10}^{-9}m$

Answer 1

The correct option is C $8.8\times {10}^{-9}m$

$l=4.5md=6\times {10}^{-3}mr=3\times {10}^{-3}mW=100NY=4.8\times {10}^{11}N{m}^{-2}\text{Poisson's Ratio}=0.2\Delta d=?$
Poisson Ratio =0.2 = $\frac{\frac{\Delta d}{d}}{\frac{\Delta l}{l}}$
$\Delta d=\frac{0.2\times d\times \Delta l}{l}$....(1)
$\frac{\Delta l}{l}=\frac{F}{A\times Y}$.....(2)
Substituting the values in (2)
$\frac{\Delta l}{l}=\frac{1}{135648}$
Substituting the value of $\frac{\Delta l}{l}$ and $d$ in (1)
$\Delta d=8.8\times {10}^{-9}m$