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Question

A steel wire of length 1 m and cross sectional area A is stretched by 1 cm under a given load. When the same load is applied to another steel wire of double length and half the cross-sectional area of the first one, the amount of stretching (extension) is

A
0.5 cm
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B
2 cm
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C
4 cm
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D
1.5 cm
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Solution

The correct option is C 4 cm
Young's modulus of elasticity is given as,
Y=stressstrain
i.e Y=(FA)(ΔLL)
ΔL=FLAYHence,ΔLLA
[since F and Y are constant here]
ΔL2ΔL1=L2L1×A1A2
Or, ΔL2ΔL1=2L1L1×A1(A12)=4
ΔL2=4×ΔL1=4×1=4 cm
Here, ΔL2 is the extension produced in the second wire.

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