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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 θ°, the twist angle at the joint will be:

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$\frac{8 θ}{9}$

$\frac{θ}{2}$

$\frac{5 θ}{6}$

$\frac{θ}{4}$

answer is D.

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Detailed Solution

$τ = C . θ = \frac{{πηr}^{4} θ}{2 L} = C o n s \tan t$

$\Rightarrow \frac{{πηr}^{4} (θ - θ_{0})}{2 l} = \frac{πη {(r / 2)}^{4} (θ_{0} - θ^{'})}{2 (l / 2)} \Rightarrow \frac{(θ - θ_{0})}{2} = \frac{θ_{0}}{16} \Rightarrow θ_{0} = \frac{8}{9} θ$

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