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COMEDK · Physics · 10. Mechanical Properties of Solids

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 \(\sigma\) )

  1. A \(\dfrac{40000 \sigma}{\pi Y}\)
  2. B \(\dfrac{40000 \pi}{\sigma Y}\)
  3. C \(\dfrac{400 \sigma}{\pi Y}\)
  4. D \(\dfrac{4000 \sigma}{\pi Y}\)
Verified Solution

Answer & Solution

Correct Answer

(A) \(\dfrac{40000 \sigma}{\pi Y}\)

Step-by-step Solution

Detailed explanation

The Young modulus \(Y\) is defined as the ratio of longitudinal stress to longitudinal strain. The longitudinal stress is \(\sigma_{stress} = \dfrac{F}{A} = \dfrac{F}{\pi r^2} = \dfrac{F}{\pi (d/2)^2} = \dfrac{4F}{\pi d^2}\), where \(F = 100\) N and \(d = 10\) mm = \(0.01\) m.…