question_answer

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 \[\theta {}^\circ \], the twist angle at the joint will be       [RPET 1997]

A)                 \[\theta /4\]             

B)                 \[\theta /2\]

C)                 \[5\theta /6\]          

D)                 \[8\theta /9\]

Correct Answer: D

Solution :

    \[\tau =C.\theta =\frac{\pi \eta {{r}^{4}}\theta }{2L}=\]Constant             \[\Rightarrow \frac{\pi \eta {{r}^{4}}(\theta -{{\theta }_{0}})}{2l}=\frac{\pi \eta {{(r/2)}^{4}}({{\theta }_{0}}-\theta ')}{2(l/2)}\]             \[\Rightarrow \frac{(\theta -{{\theta }_{0}})}{2}=\frac{{{\theta }_{0}}}{16}\Rightarrow {{\theta }_{0}}=\frac{8}{9}\theta \]