Question

One end of a nylon rope of length \( 1 \) and diameter \( 10 \, \text{mm} \) is fixed to free limb. A monkey weighing \( 100 \, \text{N} \) 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 \( \sigma \))

• A. \( \frac{4000\sigma}{\pi Y} \)
• B. \( \frac{400\sigma}{\pi Y} \)
• C. \( \frac{40000\sigma}{\pi Y} \)
• D. \( \frac{40000\pi}{\sigma Y} \)

Hint:

Poisson ratio connects lateral strain with longitudinal strain. First calculate stress, then longitudinal strain, and finally change in diameter.

Answer 1

The Correct Option is C