First slide

Elastic behaviour of solids

Question

Two wires of the same material and length but diameters in the ratio 1:2 are stretched by the same force. The potential energy per unit volume for the two wires when stretched will be in the ratio

Moderate

A

16:1
B

4:1
C

2:1
D

1:1

Solution

$Energy density = \frac{1}{2} \times Stress \times Strain$
$= \frac{1}{2} \times Stress \times \frac{Stress}{Y} = \frac{(Stress)^{2}}{2 Y} \propto \frac{1}{D^{4}}$
$Now, \frac{u_{A}}{u_{B}} = \frac{D_{B}^{4}}{D_{A}^{4}} = [2]^{4} = 16$

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