Laws Of Motion Question 140
Question: The upper half of an inclined plane with inclination $ \phi $ is perfectly smooth while the lower half is rough. A body starting from rest at the top will again come to rest at the bottom if the coefficient of friction for the lower half is given by
Options:
A) $ 2\tan \phi $
B) $ \tan \phi $
C) $ 2sin\phi $
D) $ 2\cos \phi $
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Answer:
Correct Answer: A
Solution:
[a] For first half acceleration $ =gsin\phi $
Therefore, velocity after travelling half distance $ v^{2}=2(gsin\phi )l $ (i)
For second half, acceleration $ =g(sin\phi -{{\mu } _{k}}cos\phi ) $
So $ 0^{2}=v^{2}+2g(sin\phi -{{\mu } _{k}}cos\phi )l $ (ii) Solving (i) and (ii), we get $ {{\mu } _{k}}=2\tan \phi $
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