Q 11-04-023JEE MainAIEEE 2011Medium
The minimum force required to start pushing a body up a rough (frictional coefficient $\mu$) inclined plane is $F_1$ while the minimum force needed to prevent it from sliding down is $F_2$. If the inclined plane makes an angle $\theta$ with the horizontal such that $\tan\theta = 2\mu$, then the ratio $\dfrac{F_1}{F_2}$ is
Answer: (D) $3$
Concept. $F_1=mg(\sin\theta+\mu\cos\theta)$ to push up, $F_2=mg(\sin\theta-\mu\cos\theta)$ to hold. Divide by $mg\cos\theta$.
Step 1. Ratio.
$$\frac{F_1}{F_2}=\frac{\tan\theta+\mu}{\tan\theta-\mu}=\frac{2\mu+\mu}{2\mu-\mu}=3$$
Answer. $3$ (Option D).
Solution by Sreeraj P, M.Sc Physics
