Q141 / 180 · AIIMS 2008 · Physics
If a wire is extended to a new length \(l\), the work done is
- A\(\frac{Y A}{l}\left(l-l^{\prime}\right)\)
- B\(\frac{Y A}{l}\left(l-l^{\prime}\right)^2\)
- Correct answerC\(\frac{1}{2} \frac{Y A}{l}\left(l-l^{\prime}\right)^2\)
- D\(2 \cdot \frac{Y A}{l}\left(l-l^{\prime}\right)^2\).
Solution
$Y=\frac{F / A}{\frac{\Delta l}{l}}$
$\therefore F=\frac{Y A}{l} \cdot \Delta l=k \cdot \Delta l$
Force $\propto$ extension
If the extension is $x$, work done in extending by $d x$
$\therefore F=\frac{Y A}{l} \cdot \Delta l=k \cdot \Delta l$
If $x$ is $\left(l^{\prime}-l\right), W=\frac{1}{2} k\left(l^{\prime}-l\right)^2$
i.e. work done is $\frac{1}{2} \frac{Y A}{l}\left(l-l^{\prime}\right)^2$.
Hence, the correct answer is option: 'C'.