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8.Mechanical Properties of Solids
medium
A wire of length $L$ and cross-sectional area $A$ is made of a material of Young's modulus $Y.$ It is stretched by an amount $x$. The work done is
A
$\frac{{YxA}}{{2L}}$
B
$\frac{{Y{x^2}A}}{L}$
C
$\frac{{Y{x^2}A}}{{2L}}$
D
$\frac{{2Y{x^2}A}}{L}$
Solution
(c) Work done is equal to the potential energy stored in the wire.
$\therefore \quad W=U=\frac{1}{2} \times$ Stress $\times$ Strain $\times$ Volume
OR $\quad W=\frac{1}{2} \times Y(\text { Strain })^{2} \times$ Volume $……(1)$
$(\text {Strain}=Y \times$Strain)
Strain $=\frac{x}{L}$and volume $=A L$
$\therefore W=\frac{1}{2} \times Y \times \frac{x^{2}}{L^{2}} \times A L \quad \Longrightarrow W=\frac{Y x^{2} A}{2 L}$
Standard 11
Physics
