Question

The breaking stress of a wire of length $l$ and radius r is $5\,\,kg\,\,wt/{{m}^{2}}$ . The wire of length $2l$ and radius 2r of the same material will have breaking stress in $(kwt/{{m}^{2}})$ :

• A. 5
• B. 20
• C. 80
• D. 10

Answer 1

Answer: (D)

10

Answer 2

From the formula $F=\frac{YA\,\Delta L}{L}$ ${{F}_{breaking\,stress}}\propto \frac{Y\pi {{r}^{2}}}{L}$ Hence, $\frac{5}{{{F}_{2}}}=\frac{\frac{Y\pi {{r}^{2}}}{L}}{\frac{Y\pi (4{{r}^{2}})}{2L}}=\frac{1}{2}$ Therefore, ${{F}_{2}}=10\,kwt\text{/}{{m}^{2}}$