question_answer

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                                         [AIEEE 2005]

A) \[2\sin \phi \]

B) \[2\cos \phi \]

C) \[2\tan \phi \]

D) \[\tan \phi \]

Correct Answer: C

Solution :

[c] According to work-energy theorem,

(initial and final speeds are zero)

Work done by friction + Work done by gravity =0

\[-\,(\mu \,mg\,cos\phi )\,\frac{l}{2}\,+mgl\,\sin \phi =0\]

(friction will start at 1/2)

or