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Question

A wire of length 1 m is stretched by a force of 10 N. The area of cross-section of the wire is 2×106 m2 and Young's modulus (Y) is 2×1011 N/m2. Increase in length of the wire will be -

A
2.5×105 cm
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B
2.5×105 mm
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C
2.5×105 m
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D
None of these
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Solution

The correct option is C 2.5×105 m
As we know,

Young's modulus (Y)=StressStrain=FAΔLL

Stress=FA=10(2×106)=5×106 N/m2

From Y=StressStrain

2×1011=5×106ΔLL

ΔLL=2.5×105

ΔL=1×2.5×105

ΔL=2.5×105 m

Hence, option (C) is the correct answer.
Why this Question?
Key point: Youngs modulus of elasticity is given by,

Young's modulus (Y)=StressStrain=FAΔLL

Y=FLAΔL


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