Wave Mechanics Question 511
Question: 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 $ ( \frac{Angle,of,twist,at,the,end,of,A}{Angle,of,twist,at,the,end,of,B} ) $
Options:
A) $ r _{1}^{2}/r _{2}^{2} $
B) $ r _{1}^{3}/r _{2}^{3} $
C) $ r _{2}^{4}/r _{1}^{4} $
D) $ r _{1}^{4}/r _{2}^{4} $
Show Answer
Answer:
Correct Answer: C
Solution:
[c] Couple per unit angle of twist, $ C=\frac{\pi \eta r^{4}}{2\ell } $
$ \
Therefore Couple\tau =C\theta =\frac{\pi \eta r^{4}\theta }{2\ell } $ Here $ \eta $ , $ \ell $ , C & $ \tau $ are same. So, $ r^{4}\theta = $ constant
$ \
Therefore ,\frac{{\theta _{1}}}{{\theta _{2}}}=( \frac{r _{2}^{4}}{r _{1}^{4}} ) $
BETA
