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Question

A wire of length L and radius r is clamped at one end. On stretching the other end of the wire with a force F, the increase in its length is l. If another wire of same material but of length 2L and radius 2r is stretched with a force 2F, the increase in its length will be:

A
l4
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B
l2
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C
l
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D
2l
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Solution

The correct option is C l
Let Y be Young's modulus of the material of the wire, Then for the first wire
Y=F/πr2l/L=FLπr2l...(i)
As both the wires are made of the same material, so their
Young modulus is same
Let the extension produced in second wire be l. Then
Y=2F/π(2r)2l/2L=FLπr2l...(ii)
Equating (i) and (ii) ,we get
FLπr2l=FLπr2lorl=l

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