NEET Solved Paper 2014 Question 10
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 [AIPMT 2014]
Options:
A) 5 : 7
B) 2 : 3
C) 2 : 5
D) 7 : 5
Show Answer
Answer:
Correct Answer: A
Solution:
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{g,sin\theta }{1+\frac{(2/5)R^{2}}{R^{2}}} $ $ [ \therefore for,solid,sphere,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} $
