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