When an elastic material with young's modulus 'Y' is subjected to a stretching stress 's' the elastic energy stored per unit volume is

Question

When an elastic material with young's modulus 'Y' is subjected to a stretching stress 's' the elastic energy stored per unit volume is (A) (s2/2y) (B) (ys2/2) (C) (s/2y) (D) (ys/2)

Tardigrade Admin · Accepted Answer

Given, Young's modulus = Y, Streaching stress = S, Energy stored per unit volume is, =(1/2) × stress × strian We know that, stress = strain × Y Therefore energy per unit volume will be E =(1/2) × S × ( S / Y )=( S 2/2 Y )

Q. When an elastic material with young's modulus 'Y' is subjected to a stretching stress 's' the elastic energy stored per unit volume is

$\frac{s ^{2}}{2 y}$

$\frac{y s ^{2}}{2}$

$\frac{s}{2 y}$

$\frac{ys}{2}$

Given,
Young's modulus $= Y$ ,
Streaching stress $= S$ ,
Energy stored per unit volume is, $= \frac{1}{2} \times$ stress $\times$ strian
We know that, stress $=$ strain $\times Y$
Therefore energy per unit volume will be $E = \frac{1}{2} \times S \times \frac{S}{Y} = \frac{S ^{2}}{2 Y}$