First slide

Elastic behaviour of solids

Question

The amount of workdone in increasing the length of a wire through 1cm will be

Moderate

A

$\frac{Y A}{2 L}$
B

$\frac{Y L}{2 A}$
C

$\frac{Y L^{2}}{2 A}$
D

zero

Solution

$W = \frac{1}{2} \times s t r e s s \times s t r a i n \times v o l u m e$
     $= \frac{1}{2} \times (Y \times s t r a i n) \times s t r a i n \times v o l u m e = \frac{1}{2} \times {Y \times (s t r a i n)}^{2} \times v o l u m e$
     $= \frac{1}{2} Y {(ℓ / L)}^{2} A L$
     $= \frac{1}{2} (Y A / L) ℓ^{2} = \frac{1}{2} (Y A / L) {(1)}^{2} = \frac{Y A}{2 L}$

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