Q. Two rods A and B of the same material and length have their radii $r_{1}\ and\ r_{2}$ respectively. When they are rigidly fixed at one end and twisted by the same couple applied at the other end, the ratio of the angle of twist at the end of A and the angle of twist at the end of B is
A) $\frac{r_{2}^{4}}{r_{1}^{4}}$
B) $\frac{r_{1}^{4}}{r_{2}^{4}}$
C) $\frac{r_{2}^{2}}{r_{1}^{2}}$
D) $\frac{r_{1}^{2}}{r_{2}^{2}}$
Explanation
(a) $\tau = \frac{\pi\eta r^{4}}{2l}\ \theta$
In the given problem, $r^{4}\theta =$ constant
$\therefore\ \ \frac{\theta_{A}}{\theta_{B}} = \frac{r_{2}^{4}}{r_{1}^{4}}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.