When a force is applied at one end of an elastic wire, it produces a strain $ϵ$ in the wire. If $Y$ is Young's modulus of the material of the wire, the amount of energy stored per unit volume of the wire is given by

$Y ϵ$

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$\frac{Y ϵ}{2}$

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$Y ϵ^{2}$

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$\frac{Y ϵ^{2}}{2}$

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Solution

The correct option is D
$\frac{Y ϵ^{2}}{2}$

Energy stored per unit volume $= \frac{1}{2}$ (stress $\times$ strain).
But stress = Young's modulus $\times$ strain = $Y ϵ$
Hence, energy stored per unit volume $= \frac{Y ϵ^{2}}{2}$ , which is choice (d).

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When a force is applied at one end of an elastic wire, it produces a strain ϵ in the wire. If Y is Young's modulus of the material of the wire, the amount of energy stored per unit volume of the wire is given by

The correct option is D Yϵ22 Energy stored per unit volume =12 (stress × strain). But stress = Young's modulus × strain = Yϵ Hence, energy stored per unit volume =Yϵ22, which is choice (d).

When a force is applied at one end of an elastic wire, it produces a strain $ϵ$ in the wire. If $Y$ is Young's modulus of the material of the wire, the amount of energy stored per unit volume of the wire is given by

The correct option is D
$\frac{Y ϵ^{2}}{2}$

Energy stored per unit volume $= \frac{1}{2}$ (stress $\times$ strain).
But stress = Young's modulus $\times$ strain = $Y ϵ$
Hence, energy stored per unit volume $= \frac{Y ϵ^{2}}{2}$ , which is choice (d).