Question

Two cylinders A and B of the same material have same length, their radii being in the ratio of $1:2$, respectively. The two are joined end to end as shown. The upper end of A is rigidly fixed. The lower end of B is twisted through an angle $\theta$, the angle of twist of the cylinder A is

• A. $\frac{15}{16}\theta$
• B. $\frac{16}{15}\theta$
• C. $\frac{16}{17}\theta$
• D. $\frac{17}{16}\theta$

Answer 1

The correct option is C $\frac{16}{17}\theta$

Twisting Couple or Restoring Torque $G=\frac{\pi \eta r^4}{2l}\theta$ , where $\theta$ is the angle of twist.

$\therefore \frac{{\theta }_A}{{\theta }_B}=\frac{{r_B}^4}{{r_A}^4}$

$\frac{{\theta }_A}{{\theta }_B}=16$

Given: ${\theta }_A+{\theta }_B=\theta$

${\theta }_A=\frac{16}{17}\theta$