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Question: The elastic energy stored per unit volume in a stretched wire is...

The elastic energy stored per unit volume in a stretched wire is

A

12stressY\frac{1}{2}\frac{\text{stress}}{Y}

B

12(stress)2Y.\frac{1}{2}\frac{(\text{stress})^{2}}{Y}.

C

12(stress)2Y2\frac{1}{2}\frac{(\text{stress})^{2}}{Y^{2}}

D

12(stress)Y2\frac{1}{2}\frac{(\text{stress})}{Y^{2}}

Answer

12(stress)2Y.\frac{1}{2}\frac{(\text{stress})^{2}}{Y}.

Explanation

Solution

: The elastic energy stored per unit volume in a stretched wire is

u=12×stress×strain=(stress)22Yu = \frac{1}{2} \times stress \times strain = \frac{(stress)^{2}}{2Y} (∴Y=stressstrain)\left( \therefore Y = \frac{stress}{strain} \right)