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 Solved Paper-2005
A)\[2\sin \phi \]
B) \[2\cos \phi \]
C) \[2\tan \phi \]
D) \[\tan \phi \]
Correct Answer:
C
Solution :
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