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Young's Modulus of Elasticity

A wire extend...

Question

A wire extends by 1 mm when a force is applied. What will be the elongation(in mm) in wire of same material if the force is doubled on the wire of same length and half the radius?

A

8

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B

4

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C

2

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D

1

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Solution

The correct option is A 8
a) say l= elongation; L= original length; Y= modulus of elasticity. Then from Hooke's law
$l = \frac{F L}{π r^{2} Y} = l \propto \frac{F}{r^{2}}$ (Y and L are constant)
$\frac{l_{2}}{l_{1}} = \frac{F_{2}}{F_{1}} \times (\frac{r_{1}}{r_{2}})^{2} = 2 \times (2)^{2} = 8 \Rightarrow l_{2} = 8 l_{1} = 8 \times$ 1=8mm

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