Question

The upper half of an inclined plane of inclination $\theta$ is perfectly smooth while the lower half is rough $A$ body starting from the rest at top come back to rest at the bottom, then the coefficient of friction for the lower half is given by _______.

• A. ${\mu }_s=\sin \theta$
• B. ${\mu }_s=\cos \theta$
• C. ${\mu }_s=2\cos \theta$
• D. ${\mu }_s=2\tan \theta$

Answer 1

The correct option is D ${\mu }_s=2\tan \theta$

Upper half of an inclined plane of inclination $\theta$ is perfectly smooth while lower half is rough. A body starting from the rest at top comes back to rest at the bottom, then coefficient of friction of the lower half will be just double as in the case when whole incline is rough.

When whole incline is rough we know

${\mu }_S=\tan \theta$.

If half incline is smooth and half is rough then coefficient of friction must be double

${\mu }_S=2\tan \theta$