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.

Options

A. `1.327 mu m`
B. `0.151 um m`
C. `0.625 mu m`
D. ` 0.425 mu m`

Answer

A

Explanation

Here l = 9 m, D= 6 mm `= 6xx10^(-3) m`, F = 200 N, `Y= 4.8xx 10^(11) N m^(-2), sigma = 0.2`
As ` Y = (F)/(L) .(l)/(Deltal)`
`therefore Deltal = (F)/(A) .(l)/(Y) = (200 xx 9)/(3.14 xx (6xx 10^(-3))^(2) xx 4.8 xx 10^(11))`
`= 13.269 xx 10^(-5)m`