If x longitudinal strain is produced in a wire of Young's modulus y, then energy stored in mater

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8.Mechanical Properties of Solids

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If $x$ longitudinal strain is produced in a wire of Young's modulus $y,$ then energy stored in the material of the wire per unit volume is

A

$y{x^2}$

B

$2\,y{x^2}$

C

$\frac{1}{2}{y^2}x$

D

$\frac{1}{2}y{x^2}$

(AIIMS-2001)

Solution

(d) Energy stored per unit volume

$ = \frac{1}{2} \times {\rm{Stress}} \times {\rm{Strain}}$

$ = \frac{1}{2} \times {\rm{Young's\, modulus }} \times {{\rm{(Strain)}}^{\rm{2}}} = \frac{1}{2} \times Y \times {x^2}$

Standard 11

Physics

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