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. $\frac{s^2}{2y}$
• B. $\frac{ys^2}{2}$
• C. $\frac{s}{2y}$
• D. $\frac{ys}{2}$

Answer 1

Answer: (A)

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 $E =\frac{1}{2} \times S \times \frac{ S }{ Y }=\frac{ S ^{2}}{2 Y }$