Two wires A and B of same length and of the same material have the respective radii $\Gamma_1$ and $\Gamma_{2}$ . 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
$(a) \frac{r_1^2}{r_2^2} \quad (b) \frac{r_2^2}{r_1^2} \quad (c) \frac{r_2^4}{r_1^4} \quad (d) \frac{r_1^4}{r_2^4}$
Text Solution
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Twisting couple $c = \frac{\pi \eta r^{4} \theta}{2l}$
If material and length of the wires A and B are equal and equal twisting couple are applied then
$\theta \propto \frac{1}{r^{4}}$ ∴ ∴ $\frac{\theta_1}{\theta_2} = \left(\frac{r_2}{r_1}\right)^4$
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