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Q.

A wire of length 'L' and radius 'r' is fixed at one end and a force 'F' is applied to the other end to produce an extension '2l'. The extension produced in another wire of same material of length '2L' and radius '2r' by a force '2F' is --

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a

4l

b

2l

c

l/2

d

l

answer is B.

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Detailed Solution

$e_{2} = ℓ$

$\frac{F_{1} ℓ_{1}}{r_{1}^{2} e_{1}} = \frac{F_{2} ℓ_{2}}{r_{2}^{2} e_{2}}$ ( as both are made of same material)

$\frac{F L}{r_{}^{2} 2 ℓ} = \frac{2 F 2 L}{{(2 r)}^{2} e_{2}} \Rightarrow e_{2} = 2 ℓ$

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A wire of length 'L' and radius 'r' is fixed at one end and a force 'F' is applied to the other end to produce an extension '2l'. The extension produced in another wire of same material of length '2L' and radius '2r' by a force '2F' is --