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8.Mechanical Properties of Solids
medium
A block of mass $M$ is suspended from a wire of length $L$, area of cross-section $A$ and Young's modulus $Y$. The elastic potential energy stored in the wire is
A
$\frac{1}{2}\frac{{{M^2}{g^2}L}}{{AY}}$
B
$\frac{1}{2}\frac{{Mg}}{{AYL}}$
C
$\frac{1}{2}\frac{{{M^2}{g^2}A}}{{YL}}$
D
$\frac{1}{2}\frac{{MgY}}{{AL}}$
Solution
$U=\frac{1}{2}(\text { stress })$ (strain) (volume) $=\frac{1}{2}$ (stress)
$\left[\frac{\text { stress }}{Y}\right]$ (volume) $=\frac{1}{2}\left[\frac{\text { stress }^{2}}{Y}\right] \times$ volume
$=\frac{1}{2}\left[\frac{M g}{A}\right]^{2} \cdot\left[\frac{1}{Y}\right](A L)=\frac{1}{2} \frac{M^{2} g^{2} L}{A Y}$
Standard 11
Physics
