First slide

Elastic behaviour of solids

Question

If the work done by stretching a wire by 1 mm is 2 J, the work necessary for stretching another wire of the same material but with double the radius of cross section and half the length by 1 mm is

Moderate

A

$\frac{1}{4} J$
B

4 J
C

8 J
D

16 J

Solution

$\begin{array}{l} W = \frac{1}{2} FΔl \\ W = \frac{1}{2} \times \frac{{Yπr}^{2} Δl}{l} Δl and Y = \frac{Fl}{{πr}^{2} Δl} \\ or W = \frac{{Yπr}^{2} {Δl}^{2}}{2 l} and F = \frac{{Yπr}^{2} Δl}{l} \\ or W \propto \frac{r^{2}}{l}, W^{'} \propto \frac{(2 r)^{2} 2}{l} \\ \frac{W^{'}}{W} = 8 or W^{'} = 8 \times 2 J = 16 J \end{array}$

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