A wire of length L and radius r is clamped rigidly at one end. When the other end of the wire is pulled by a force f , its length increases by l . Another wire of same material of length 2 L and radiu

Question

A wire of length L and radius r is clamped rigidly at one end. When the other end of the wire is pulled by a force f , its length increases by l . Another wire of same material of length 2 L and radius 2 r is pulled by a force 2 f . Then the increase in its length will be:

TestHub · Accepted Answer

Young's modulus is same for both the wires since the material is same.
For the first wire,
$Y = \frac{f L}{π r^{2} l} . . . (i)$
For the second wire,
$Y = \frac{2 f (2 L)}{4 π r^{2} l'} . . . (i i)$
Dividing (i) by (ii)
$\frac{f L}{π r^{2} l} \times \frac{4 π r^{2} l'}{4 f L} = 1 \Rightarrow l' = l$

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