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Question

A wire is stretched by 0.01 m by a certain force F. Another wire of same material whose diameter and lengths are doubled to the original wire is stretched by the same force. Then its elongation will be:

A
0.005 m
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B
0.01 m
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C
0.02 m
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D
0.08 m
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Solution

The correct option is A 0.005 m

Given that,

Δl1=0.01m

Length l1=l

Length l2=2l

Radius r1=r

Radius r2=2r

We know that,

Y=FlAΔl

Δl=Flπr2Y

Δllr2

Now, the diameter and lengths are doubled to the original wire is stretched by the same force

So,

Δl2Δl1=2ll×r24r2

Δl2Δl1=2×14

Δl2=0.012

Δl2=0.005m

Hence, the elongation is 0.005 m


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