First slide

Elastic behaviour of solids

Question

What amount of work is done in increasing the length of a wire through unity?

Moderate

A

$\frac{YL}{2 A}$
B

$\frac{{YL}^{2}}{2 A}$
C

$\frac{YA}{2 L}$
D

$\frac{YL}{A}$

Solution

$Work done = \frac{1}{2} F \times Extension$
$\begin{array}{l} = \frac{1}{2} \times \frac{YA}{L} \times 1 \\ = \frac{YA}{2 L} \end{array}$ $\begin{array}{l} [Y = \frac{F \times L}{A \times 1} \Rightarrow F = \frac{YA}{L}] \end{array}$

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