Q. 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 $\theta$ from the horizontal such that $\tan{\theta = 2\mu}$, then the ratio $\frac{F_{1}}{F_{2}}$ is
A) 4
B) 1
C) 2
D) 3
Explanation
(d) $F_{1} = mg(\sin{\theta + \mu\cos{\theta)}}$
$F_{2} = mg(\sin{\theta + \mu\cos{\theta)}}$
$\frac{F_{1}}{F_{2}} = \frac{\sin{\theta + \mu\cos\theta}}{\sin{\theta - \mu\cos\theta}}$
$= \frac{\tan{\theta + \mu}}{\tan{\theta - \mu}}$
$= \frac{2\ \mu + \mu}{2\ \mu - \mu}$
$= 3$
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Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.