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 $\left[\frac{AngleoftwistattheendofA}{AngleoftwistattheendofB}\right]$ is:

• A. $r_1^2/r_2^2$
• B. $r_1^3/r_2^3$
• C. $r_2^4/r_1^4$
• D. $r_1^4/r_2^4$

Answer 1

The correct option is C $r_2^4/r_1^4$

Couple per unit angle of twist, $C=\frac{\pi \eta r^4}{2l}$
$\therefore$ Couple $=C\theta =\frac{\pi \eta r^4\theta }{2l}$
Here $\eta ,l,C$ &are same. So, $r^4\theta =$ constant
$\therefore \frac{{\theta }_1}{{\theta }_2}=\left[\frac{r_2^4}{r_1^4}\right]$