Wave Mechanics Question 525
Question: Two cylinders A and B of the same material have same length, their radii being in the ratio 1:2 respectively. The two are joined end to end as shown. One end of cylinder A is rigidly clamped while free end of cylinder B is twisted through an angle 9. The angle of twist of cylinder A is
Options:
A) $ \frac{16}{17}\theta $
B) $ \frac{15}{16}\theta $
C) $ 8\theta $
D) $ \frac{3}{2}\theta $
Show Answer
Answer:
Correct Answer: A
Solution:
[a] Let $ {\theta _{1}} $ and $ {\theta _{2}} $ are the angle of twist produced in cylinders A and B respectively. Given, $ {\theta _{1}}+{\theta _{2}}=\theta $ ?(i) On being in series, the torque acts at their free ends are equal. We have $ \tau =\frac{\pi \eta r^{4}\theta }{2\ell } $
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Therefore \frac{\pi \eta r^{4}{\theta _{1}}}{2\ell }=\frac{\pi \eta {{(2r)}^{4}}{\theta _{2}}}{2\ell }\Rightarrow {\theta _{1}}=16{\theta _{2}} $ ? (ii) From (i) and (ii), we have $ {\theta _{1}}=\frac{16}{17}\theta $
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