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Question

The length of a copper wire increases by 0.01 metre when loaded with 10kg weight. Another copper wire of the same length but double the radius is loaded with the same weight. The increase in length of the second wire in metres will be

A
0.002
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B
0.005
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C
0.0025
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D
0.01
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Solution

The correct option is C 0.0025
Given, increase in length (ΔL)=0.01 m when load is Let length =Lm radius =r
young's modulus = Stress strain
y=(FA)(ΔLL)y=10×10×Lπr2×0.01
y=104Lπr2(1)
when, r becomes 2r Load remains same
TY=FL4πr2(ΔL)new (11)
(i) = (ii) 104 Lπr2=102 L4πr2(ΔL)new
(ΔL)new =1400 mΔL=0.0025 m

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