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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