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Question

Two wires are made of the same material and have the same volume. The first wire has a cross-sectional area 1 mm2 and the second wire has cross-sectional area 4 mm2. If the length of the first wire is increased by ΔL on applying a force of 10 N, how much force is needed to stretch the second wire by the same amount?

A
160 N
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B
100 N
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C
90 N
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D
80 N
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Solution

The correct option is A 160 N
To stretch the second wire through same length (ΔL), let force needed be F
Young's modulus should be same for both cases due to same material of wire
Y=(F/A)(ΔL/L)
F/AΔL/L=F/AΔL/L ...(i)
Since,volume is same
A×L=AL
LL=AA=41 ...(ii)
From Eq. (i) & (ii),
FLA=FLA
F=AA×LL×F
F=(41)2×F
F=16×10=160 N

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