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  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