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Question

# The length of a metal wire is 3.75 m when the tension in it is 100 N and is 3.50 m when the tension is 80 N. The natural length of the wire ( in cm) is

A
250.0
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B
250
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C
250.00
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Solution

## Given, Length of wire when the tension is 100 N (l1)=3.75 m. Length of wire when the tension is 80 N (l2)=3.50 m. Let us suppose, the natural length of the wire be L m. When tension is 100 N, change in length of wire (ΔL)=l1−L=3.75−L We know that, Young's modulus (Y)=F×LA×ΔL ⇒Y=100×LA×(3.75−L) ..............(1) Change in length of wire when tension is 80 N ΔL=l2−L=3.50−L Again using the formula of Young's modulus, Y=F×LA×ΔL ⇒Y=80×LA×(3.50−L)...........(2) From (1) and (2) as the material is same, we can write that, 100×LA×(3.75−L)=80×LA×(3.50−L) ⇒350−100L=300−80L ⇒L=2.5 m or 250 cm

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