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Question

Physics Question on Elastic and inelastic collisions

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

A

12\frac{1}{2} (Young's modulus) (Strain)2^{2}

B

12\frac{1}{2} (Stress) (Strain) 2^{2}

C

12StressStrain\frac{1}{2}\frac{\text{Stress}}{\text{Strain}}

D

12\frac{1}{2} (Young modulus) (Stress)

Answer

12\frac{1}{2} (Young's modulus) (Strain)2^{2}

Explanation

Solution

The energy stored in per unit volume of wire
(UV)=12Fl volume =12×\left(U_{V}\right)=\frac{1}{2} \frac{F l}{\text { volume }}=\frac{1}{2} \times stress ×\times strain
=12×Y×( strain )2=12Y( stress )2=\frac{1}{2} \times Y \times(\text { strain })^{2}=\frac{1}{2 Y}(\text { stress })^{2}