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 =2mu` then the ratio `(F_(1))/(F_(2))` is .

Options

A. 4
B. 1
C. 2
D. 3

Answer

D

Explanation

The minimum force required to start pushing a body up a rough inclined plane is
`F_(1)=mg sintheta+mumg sintheta....(i)`
Minimum force needed to prevent the body from sliding down the inclined plane is
`F_(2)=mg sintheta+mumg sintheta....(ii)`
Divide (i) by (ii), we get
`(F_(1))/(F_(2))=(sintheta+mu costheta)/(sintheta-mu costheta)=(tan theta+mu)/(tan theta-mu)`
`=(2mu+u)/(2mu-u)=3 (therefore tan theta=2mu ("Given"))`