Q.
Two cylinders of same material and of same length are joined to end as shown in figure. The upper end of A is rigidly fixed. Their radii are in ratio of 1 : 2, If the lower end of B is twisted by an angle $\theta,\ $the angle of twist of cylinder A is
A) $\frac{15}{16}\theta$
B) $\frac{16}{15}\theta$
C) $\frac{16}{17}\theta$
D) $\frac{17}{16}\theta\ $
Explanation
(c) For cylinder A,
$\tau = \frac{\pi\eta r^{4}}{2l}\ \theta^{'}$
For cylinder $B,\ \ \ \tau = \ \frac{\pi\eta(2r)^{4}(\theta - \theta^{'})}{2l}$
$\frac{\pi\eta r^{4}\theta^{'}}{2l\ } = \ \frac{\pi\eta(2r)^{4}(\theta - \theta^{'})}{2l}$
$\theta^{'} = \frac{16}{17}\ \theta$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.