If in a wire of Young’s modulus Y , longitudinal strain X is produced then the potential energy stored in its unit volume will be

Question

If in a wire of Young’s modulus Y , longitudinal strain X is produced then the potential energy stored in its unit volume will be (A)  0.5 Y X 2  (B)  0.5 Y2 X  (C)  2 Y X2  (D)  Y X2

Tardigrade Admin · Accepted Answer

Elastic potential energy per unit volume

U = \frac{1}{2} \times stress \times strain

From definition of Young's modulus of wire

Y = \frac{stress}{strain}

\Rightarrow

Stress

= Y \times

strain
Given, strain=X
=

U = \frac{1}{2} T X^{2}

\Rightarrow U = 0.5 Y X^{2}

Q. If in a wire of Young’s modulus $Y$ , longitudinal strain $X$ is produced then the potential energy stored in its unit volume will be

$0.5 Y X^{2}$

$0.5 Y^{2} X$

$2 Y X^{2}$

$Y X^{2}$

Elastic potential energy per unit volume
$U = \frac{1}{2} \times stress \times strain$
From definition of Young's modulus of wire
$Y = \frac{stress}{strain}$
$\Rightarrow$ Stress $= Y \times$ strain
Given, strain=X
= $U = \frac{1}{2} T X^{2}$
$\Rightarrow U = 0.5 Y X^{2}$

Q. If in a wire of Young’s modulus Y , longitudinal strain X is produced then the potential energy stored in its unit volume will be

0.5YX2

0.5Y2X

2YX2

YX2