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 $\theta°$, the twist angle at the joint will be
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(d) $\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{{\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 $
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