Physics Elasticity Question 47
Question: 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]
Options:
A) $ \theta /4 $
B) $ \theta /2 $
C) $ 5\theta /6 $
D) $ 8\theta /9 $
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Answer:
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 $
BETA
