Question

A rod of length $l \, $ and radius $r$ is joined to a rod of length $\frac{l}{2}$ and radius 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 $\theta ^{0}$ , the twist angle at the joint will be

• A. $\frac{\theta }{4}$
• B. $\frac{\theta }{2}$
• C. $\frac{5 \, \theta }{6}$
• D. $\frac{8 \, \theta }{9}$

Answer 1

Answer: (D)

$\tau=C\theta $
$=\frac{\pi ɳ r^{4} \theta }{2 L}=constant$
⟹ $\frac{\left(\theta - \left(\theta \right)_{0}\right)}{2}=\frac{\left(\theta \right)_{0}}{16}$
⟹ $ \, \, \, \theta _{0}=\frac{8}{9}\theta $