Question

A rod of length $l$ and radius $r$ is joined to a rod of length $l/2$ and radius $r/2$ of same material. The free end of small rod is fixed to a rigid base and the free end of larger rod is given a twist of ${\theta }^o$, the twist angle at the joint will be

• A. $\theta /4$
• B. $\theta /2$
• C. $5\theta /6$
• D. $8\theta /9$

Answer 1

The correct option is D $8\theta /9$

$r=C.\theta =\frac{\pi \eta r^4\theta }{2L}=constant$
$\Rightarrow \frac{\pi \eta r^4(\theta -{\theta }_0)}{2l}=\frac{\pi \eta \left(r/2{)}^4\right({\theta }_0-{\theta }^{\prime })}{2\left(l/2\right)}$
$\Rightarrow \frac{(\theta -{\theta }_0)}{2}=\frac{{\theta }_0}{16}\Rightarrow {\theta }_0=\frac{8}{9}\theta$