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Question

The length of a metal wire is l1 when the tension in it is T1 and is l2 when the tension is T2. The natural length of wire is

A
l1+l22
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B
l1l2
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C
l1T2l2T1T2T1
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D
l1T2+l2T1T2+T1
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Solution

The correct option is D l1T2l2T1T2T1
Let the natural length of wire be lo.
Using Hooke's law, Y=TloAΔl
where Δl=llo
We get llo=TloAY
Case 1 : Tension is T1 and length of wire l=l1
l1lo=T1loAY .....(1)
Case 2 : Tension is T2 and length of wire l=l2
l2lo=T2loAY .....(2)
Dividing both equations l1lol2lo=T1T2
lo=l1T2l2T1T2T1

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