Rotational Motion Question 81
Question: The ratio of the accelerations for a solid sphere (mass m and radius R) rolling down an incline of angle $ \theta $ without slipping and slipping down the incline without rolling is
Options:
A) 5 : 7
B) 2 : 3
C) 2 : 5
D) 7 : 5
Show Answer
Answer:
Correct Answer: A
Solution:
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A solid sphere rolling without slipping down an inclined plane In this case, $ a _1=\frac{g\sin \theta }{1+\frac{k^{2}}{R^{2}}}=\frac{gsin\theta }{1+\frac{(2/5)R^{2}}{R^{2}}} $
$ [ \therefore forsolidsphere,K^{2}=\frac{2}{5}R^{2} ] $
$ =\frac{g\sin \theta }{7/5} $
$ \Rightarrow $ $ a _1=\frac{5}{7}g\sin \theta $
For a sphere slipping down an inclined plane
$ \Rightarrow $ $ a _2=g\sin \theta $
$ \Rightarrow $ $ \frac{a _1}{a _2}=\frac{5/7g\sin \theta }{g\sin \theta } $
$ \Rightarrow $ $ \frac{a _1}{a _2}=\frac{5}{7} $
