If in a wire of Youngs modulus Y , longitudinal strain X is produced. Then the potential energy stored in its unit volume is

Question

If in a wire of Youngs modulus Y , longitudinal strain X is produced. Then the potential energy stored in its unit volume is (A)  0.5 YX2  (B)  0.5 Y2X  (C)  YX2  (D)  2 YX2

Tardigrade Admin · Accepted Answer

Youngs modulus =Y Bulk modulus ~=X The potential energy =(1/2)× stress × strain =(1/2)× (Y× textstrain)× textstrain =(1/2)(Y× X)× X=(1/2)YX2=0.5YX2

Q. If in a wire of Youngs modulus $Y$ , longitudinal strain $X$ is produced. Then the potential energy stored in its unit volume is

$0.5 Y X^{2}$

$0.5 Y^{2} X$

$Y X^{2}$

$2 Y X^{2}$

Youngs modulus $= Y$ Bulk modulus $= X$ The potential energy $= \frac{1}{2} \times$ stress $\times$ strain $= \frac{1}{2} \times (Y \times strain) \times strain$ $= \frac{1}{2} (Y \times X) \times X = \frac{1}{2} Y X^{2} = 0.5 Y X^{2}$

Q. If in a wire of Youngs modulus Y , longitudinal strain X is produced. Then the potential energy stored in its unit volume is

0.5YX2

0.5Y2X

YX2

2YX2