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Question

A copper wire of cross-sectional area 0.01 cm2 is under a tension of 20 N. Find the decrease in the cross-sectional area. Young's modulus and Poisson's ratio of copper are 1.1×1011 N/m2 and 0.32 respectively.

A
3.16×106 cm2
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B
1.16×106 cm2
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C
4.16×106 cm2
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D
2.16×106 cm2
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Solution

The correct option is B 1.16×106 cm2
Given:
F=20 N; A=0.01 cm2; Y=1.1×1011 N/m2
We know that Young's modulus,
Y=stressstrain
Y=F/AΔL/L
ΔLL=FAY
ΔLL=200.01×104×1.1×1011=1.8181×104

Now,
Poisson's ratio =Transvere strainLongitudnal strain=ΔddΔLL
Δdd=0.32×1.8181×104=5.8179×105

Also we know, fractional change in area
ΔAA=2Δdd
ΔAA=2×5.8179×105
ΔAA=1.1636×104
ΔA=1.1636×104×0.01
ΔA=1.1636×106 cm21.16×106 cm2
Negative sign shows the decrease in area of cross -section when tension is applied in the wire.
Hence, (b) is the correct option.

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