The elastic energy stored in a wire of Youngs modulus Y is

Question

The elastic energy stored in a wire of Youngs modulus Y is (A) (1/2) Y × stress × strain × volume (B) (( text stress )2 × text volume /2 Y) (C) stress × strain × volume (D) Y × (( text stress )2/ text volume )

Tardigrade Admin · Accepted Answer

When a wire is stretched work is done against the interatomic forces.
This work is stored in the wire in the form of elastic potential energy.

W = \frac{1}{2} \times

stress

\times

strain

\times

volume of wire
Also when strain is small, ratio of longitudinal stress to corresponding longitudinal strain is called Youngs Modulus of material of body.

Y = \frac{longitudinal stress}{longitudinal strain}

∴ W = \frac{1}{2} \times

stress

\times \frac{stress}{Y} \times

volume

= \frac{( stress ) ^{2} \times volume}{2 Y}

Q. The elastic energy stored in a wire of Youngs modulus $Y$ is

$\frac{1}{2} Y \times$ stress $\times$ strain $\times$ volume

$\frac{( stress ) ^{2} \times volume}{2 Y}$

stress $\times$ strain $\times$ volume

$Y \times \frac{( stress ) ^{2}}{volume}$

Q. The elastic energy stored in a wire of Youngs modulus Y is

21​Y× stress × strain × volume

2Y( stress )2× volume ​

stress × strain × volume

Y× volume ( stress )2​

Q. The elastic energy stored in a wire of Youngs modulus $Y$ is

$\frac{1}{2} Y \times$ stress $\times$ strain $\times$ volume

$\frac{( stress ) ^{2} \times volume}{2 Y}$

stress $\times$ strain $\times$ volume

$Y \times \frac{( stress ) ^{2}}{volume}$