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.

Answer

`3.315 xx 10^(-5) m ; 8.84 xx 10^(-9)m`

Explanation

Here, `l = 4.5 m, D = 6 mm = 6xx 10^(-3) m,`
`F = Mg = 100 N`
`Y = 4.8xx10^(11) N//m^2 , Delta l = ? , Delta D = ?`
`Y =(F)/((pi D^2//4)) xx(l)/(Delta l)`
` or Delta l = (4F l)/(pi D^2 Y) = (4xx100 xx 4.5)/(3.14 xx (6xx 10^(-3))^2 xx (4.8 xx 10^(11))`
` =3.315xx 10^(-5) m`
`sigma = (Delta D)/(D)/(Delta l//l) ("in magnitude")`
`Delta D = sigma (Delta l)/(l) xx D = 0.2 xx (3.315 xx 10^(-5))/(4.5) xx(6xx 10^(-3))`
` =8.84xx 10^(-9)m`