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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 the wire is :

A
l1+l22
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B
l1l2
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C
l1T2l2T1T2T1
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D
l1T2+l2T1T1+T2
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Solution

## The correct option is C l1T2−l2T1T2−T1If Δl be the elongation due to tension T, then T∝Δl Thus, T1∝Δl1 and T2∝Δl2 where l= natural length of wire.So, T1T2=Δl1Δl2....(1)Now, l1=l+Δl1 and l2=l+Δl2So, l1T2=T2l+T2Δl1...(2) andl2T1=T1l+T1Δl2...(3)using (1), (3) becomes l2T1=T1l+T2Δl1...(4)(2)−(4)→l1T2−l2T1=T2l−T1lor l=l1T2−l2T1T2−T1

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