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\,\,Y{{X}^{2}} $
• B. $ 0.5\,\,{{Y}^{2}}X $
• C. $ Y{{X}^{2}} $
• D. $ 2\,\,Y{{X}^{2}} $

Answer 1

Answer: (A)

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