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)

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}} $