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 the top comes back to rest at the bottom if the coefficient of friction for the lower half is given by

• A. $\mu =sin\theta$
• B. $\mu =cot\theta$
• C. $\mu =2cos\theta$
• D. $\mu =2tan\theta$

Answer 1

Answer: (D)

For the upper half

$v^2=u^2+2al/2=2(gsin\theta )l/2=glsin\theta$ For lower half $\Rightarrow$ $0=u^2+2g(sin\theta -\mu cos\theta )\frac{l}{2}$ $\Rightarrow$ $-glsin\theta =gl(sin\theta -\mu cos\theta )$ $\Rightarrow$ $\mu cos\theta =2sin\theta \Rightarrow \mu =2tan\theta$