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)

$\tau =C\theta$
$=\frac{\pi ɳr^4\theta }{2L}=constant$
⟹ $\frac{\left(\theta -{\left(\theta \right)}_0\right)}{2}=\frac{{\left(\theta \right)}_0}{16}$
⟹ ${\theta }_0=\frac{8}{9}\theta$