Q 11-04-024NEETJEE MainEAMCET 2014 (Engineering)Medium
The force required to move a body up a rough inclined plane is double the force required to prevent the body from sliding down the plane. The coefficient of friction when the angle of inclination of the plane is $60°$ is
Answer: (B) $\dfrac{1}{\sqrt{3}}$
Concept. Up-force $mg(\sin\theta + \mu\cos\theta)$; holding force $mg(\sin\theta - \mu\cos\theta)$.
Step 1. Equation. $\sin\theta + \mu\cos\theta = 2(\sin\theta - \mu\cos\theta) \Rightarrow 3\mu = \tan\theta$.
Step 2. Solve. $\mu = \dfrac{\sqrt3}{3} = \dfrac{1}{\sqrt3}$.
Answer. $\dfrac{1}{\sqrt3}$ (Option B).
Solution by Sreeraj P, M.Sc Physics