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Question

Two wires are made of the same material and have the same volume. However, wire 1 has cross - sectional area A and wire-2 has cross - sectional area 3A. If the length of wire 1 increases by Δx on applying force F, how much force is needed to stretch wire 2 by the same amount?

A
F
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B
4F
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C
6F
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D
9F
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Solution

The correct option is D 9F
Two wires are made of the same material and have the same volume.
A1l1=A2l2l2=A1l1A2=A×l13A=l13
l1l2=3

We know that, change in length Δl=FAγ×l
where γ=Young's modulus.
For wire 1;
Δx1=F1Aγ×l1......(i)
For wire 2;
Δx2=F23Aγ×l2.....(ii)
Here Δx1=Δx2
F23Aγl2=F1Aγl1
F2=3F1×l1l2
Put the value of l1l2 here
=3F1×3=9F

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