JEE Main & Advanced Physics Elasticity Question Bank Youngs Modulus and Breaking Stress

  • question_answer
    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 [MP PMT 1987, 89, 92; CPMT 1997; Pb. PMT 1999; KCET 2000; AIIMS 2001]

    A)                 \[y{{x}^{2}}\]    

    B)                 \[2\,y{{x}^{2}}\]

    C)                 \[\frac{1}{2}{{y}^{2}}x\]

    D)                 \[\frac{1}{2}y{{x}^{2}}\]

    Correct Answer: D

    Solution :

        Energy stored per unit volume\[=\frac{1}{2}\times \text{Stress}\times \text{Strain}\]             \[=\frac{1}{2}\times \text{Young }\!\!'\!\!\text{ s modulus }\times {{\text{(Strain)}}^{\text{2}}}=\frac{1}{2}\times Y\times {{x}^{2}}\]


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