The minimum force required to start pushing a body up a rough (fr… - Vidyadip

MCQ

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
$2$
✓
$3$

✓

Answer

Correct option: D.

$3$

d
$F _{1}= mg (\sin \theta+\mu \cos \theta)$

$F _{2}= mg (\sin \theta-\mu \cos \theta)$

$\frac{ F _{1}}{ F _{2}}=\frac{\sin \theta+\mu \cos \theta}{\sin \theta-\mu \cos \theta}$

$\frac{ F _{1}}{ F _{2}}=\frac{\tan \theta+\mu}{\tan \theta-\mu}$

$\frac{ F _{1}}{ F _{2}}=\frac{2 \mu+\mu}{2 \mu-\mu}$

$\frac{ F _{1}}{ F _{2}}=3$

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