First slide

Elastic Modulie

Question

The elastic potential energy of a stretched wire is given by

Easy

A

$U = \frac{A L}{2 Y} l^{2}$
B

$U = \frac{A Y}{2 L} l^{2}$
C

$U = \frac{1}{2} (\frac{A L l}{Y}) l$
D

$U = \frac{1}{2} \cdot \frac{Y L}{2 A} \cdot l$

Solution

Elastic potential energy of a stretched wire is given by
$U = \frac{1}{2} \times Stress \times Strain \times Volume$
$= \frac{1}{2} \times Y \times Strain \times Strain \times Volume$
$= \frac{1}{2} \times Y \times {(\frac{l}{L})}^{2} \times A L$
$∴ U = \frac{A Y l^{2}}{2 L}$

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