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One end of a nylon rope of length 4.5 m ...

One end of a nylon rope of length 4.5 m and diameter 6 mmis fixed to a tree limb. A monkey weighing 100 N jumps to catch the free end and stays there. Find the elongation of the rope and the corresponding change in the diameter. Young modulus of nylon =0.2.

Text Solution

Verified by Experts

The correct Answer is:
8.8
Here l= 4.5m, D= 6mm= `6 xx 10^(-3)m, F= 100N`,
`Y= 4.8 xx 10^(11) Nm^(-2), sigma = 0.2`
As `Y= (F)/(A).(l)/(Delta l)`
`therefore Delta l= (F)/(A).(l)/(Y)= (100 xx 4.5)/(3.14 xx (3 xx 10^(-3))^(2) xx 4.8 xx 10^(11))`
`= 3.32 xx 10^(-5)m`
Poisson.s ratio, `sigma = (Delta D//D)/(Delta l//l)= (Delta D)/(D).(l)/(Delta l)`
`therefore Delta D= (sigma D Delta l)/(l)= (0.2 xx 6 xx 10^(-3) xx 3.32 xx 10^(-5))/(4.5)`
`= 8.8 xx 10^(-9)m`
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