Laws Of Motion Question 333
Question: The minimum force required to start pushing a body up rough (frictional coefficient u) 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
Options:
A) 1
B) 2
C) 3
D) 4
Show Answer
Answer:
Correct Answer: C
Solution:
[c] For the upward motion of the body $ mg sin \theta+ f _{1} = F _{1} $
or, $ F _{1} = mg sin \theta+\mu mg cos \theta $
For the downward motion of the body, $ mgsin\theta -f _{2}=F _{2} $
$ orF _{2}=mgsin\theta -\mu mgcos\theta $
$ \therefore \frac{F _{1}}{F _{2}}=\frac{sin\theta +\mu cos\theta }{sin\theta -\mu cos\theta } $
$ \Rightarrow \frac{\tan\theta+ \mu }{\tan\theta- \mu }= \frac{2\mu+\mu }{2\mu-\mu }=\frac{3\mu }{\mu }=3 $
