A wire extends by 1 mm when a force is applied. Double the force is applied

Question

A wire extends by 1 mm when a force is applied. Double the force is applied to another wire of same material and length but half the radius of cross-section. The elongation of the wire in mm will be

Options:

A . 8

B . 4

C . 2

D . 1

Answer: Option A
:
A

a) I = \frac{F L}{π r^{2} r} l \propto \frac{F}{r^{2}}

(Y and L are constant)

\frac{l_{2}}{l_{1}} = \frac{F_{2}}{F_{1}} \times (\frac{r_{1}}{r_{2}})^{2} = 2 \times (2)^{2} = 8

l_{2} = 8 l_{1} = 8 \times 1 = 8

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