A steel wire of length 4.7m and cross-sectional area 3.0×10−5m2 stretches by the same amount as a copper wire of length 3.5m and cross-sectional area 4.0×10−5m2 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 D1.8:1 For steel wire A1=3×10−5m2,l1=4.7m,Δl1=Δl,F1=F
For copper wire, A2=4×10−5m2,l2=3.5m,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=F3×10−5×4.7Δl....(1)
and Y2=F2×l2A2×Δl2=F×3.54×10−5×Δl....(2)
From (1) and (2), we get Y1Y2=4.7×4.0×10−53.5×3.0×10−5=1.8
So, Y1:Y2=1.8:1
Thus, option (d) is the correct answer.