Question

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

• A. 16 J
• B. 8J
• C. 4J
• D. $\frac{1}{4}J$

Answer 1

Answer: (A)

16 J

Answer 2

: Stretching force, $F = \frac{Y\pi r^{2}\Delta L}{L}$

Where the symbols have their usual meanings.

Both the wires are of same material so Y will be equal, extension in both the wires is same, so $\Delta L.$ Will be equal.

$\therefore F \propto \frac{r^{2}}{L}$

$\therefore\frac{F'}{F} = \frac{(2r)^{2}}{(L/2)} \times \frac{L}{r^{2}} = 8$

Or $F' = 8F$

Work done in stretching a wire,

$W = \frac{1}{2} \times F \times \Delta L$

For same extension

$W \propto F$

$\therefore\frac{W'}{W} = \frac{F'}{F} = 8$ (using (i))

$W' = 8W = 8 \times 2J = 16J$