Question

Two wires A and B of same length and of the same material have the respective radii r₁ and r₂. Their one end is fixed with a rigid support, and at the other end equal twisting couple is applied. Then the ratio of the angle of twist at the end of A and the angle of twist at the end of B will be

• A. $\frac{r_{1}^{2}}{r_{2}^{2}}$
• B. $\frac{r_{2}^{2}}{r_{1}^{2}}$
• C. $\frac{r_{2}^{4}}{r_{1}^{4}}$
• D. $\frac{r_{1}^{4}}{r_{2}^{4}}$

Answer 1

Answer: (C)

$\frac{r_{2}^{4}}{r_{1}^{4}}$

Answer 2

$\tau_{1} = \tau_{2}$ ⇒ $\frac{\pi\eta r_{1}^{4}\theta_{1}}{2l_{1}} = \frac{\pi\eta r_{2}^{4}\theta_{2}}{2l_{2}} \Rightarrow \frac{\theta_{1}}{\theta_{2}} = \left( \frac{r_{2}}{r_{1}} \right)^{4}$