Physics Elasticity Question 37
Question: Two wires A and B of same length and of the same material have the respective radii $ r _{1} $ and $ r _{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
[AIIMS 1980]
Options:
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}} $
Show Answer
Answer:
Correct Answer: C
Solution:
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}} $
BETA
