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Question

A steel wire of length 4.7 m and cross-sectional area 3.0×105 m2 stretches by the same amount as a copper wire of length 3.5 m and cross-sectional area 4.0×105 m2 under a given load. Find the ratio of the Young's modulus of steel to that of copper

A
1.5:2
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B
1.8:2
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C
1.5:1
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D
1.8:1
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Solution

The correct option is D 1.8:1
For steel wire
A1=3×105 m2,l1=4.7 m,Δl1=Δl,F1=F
For copper wire,
A2=4×105 m2,l2=3.5 m,Δl2=Δl,F2=F
Let Y1 and Y2 be the Young's modulus of the steel wire and copper wire, respectively.
Then, Y1=F1A1×l1Δl1=F3×105×4.7Δl ....(1)
and
Y2=F2×l2A2×Δl2=F×3.54×105×Δl ....(2)
From (1) and (2), we get
Y1Y2=4.7×4.0×1053.5×3.0×105=1.8
So, Y1:Y2=1.8:1
Thus, option (d) is the correct answer.

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