Two wires of same material and length but diameter in the ratio 1 : 3 are stretched by the same force. The potential energy per unit volume for the two wires when stretched will be in the ratio:

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1: 81

9: 1

3 : 1

81 : 1

answer is D.

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Detailed Solution

$Δl = \frac{Fl}{AY} \Rightarrow \frac{Δl}{l} = (\frac{F}{AY})$

Potential energy per unit volume $= \frac{1}{2} \times Stress \times Strain$

$u = \frac{1}{2} \times \frac{F}{A} \times \frac{F}{AY} or u \propto \frac{1}{A^{2}} or u \propto \frac{1}{d^{4}}$

$∴ \frac{u_{1}}{u_{2}} = {(\frac{d_{2}}{d_{1}})}^{4} = \frac{81}{1}$

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