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Question
A telephone wire 125 m long and 1 mm in radius is stretched to a length 125.25 m when a force of 800 N is applied. What is the value of Young’s modulus for the material of wire?
Solution
Given: L = 125 m, r = 1 mm = 1 × 10−3 m,
l = 125.25 − 125 = 0.25 m, F = 800 N
To find: Young’s modulus (Y)
Formula: Y = `"FL"/("A"l) = "FL"/(pi"r"^2l)`
Calculation: From formula,
Y = `(800 xx 125)/(3.142 xx 10^-6 xx 0.25)`
= {antilog [log 800 + log 125 – log 3.142 – log 0.25 ]} × 106
= {antilog [2.9031 + 2.0969 – 0.4972 – `bar1`.3979]} × 106
= {antilog [5.1049]} × 106
= 1.274 × 105 × 106
=1.274 × 1011 N/m2
The Young’s modulus of telephone wire is 1.274 × 1011 N/m2.
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