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. 2
B. 3
C. 4
D. 1

Answer

B

Explanation

For motion up the incline plane :
`(F_(1) - "mg sin " theta ) = mu mg (sin theta + mu cos theta ) " " …. (i)`

For motion down the inclined plane :
mg sin `theta - F_(2) = mu "mg cos" theta) " " …. (ii)`
Dividing Eqn.(i) b y Eqn. (ii) ,
`(F_(1))/(F_(2)) = (sin theta + mu cos theta)/(sin theta - mu cos theta )`
=`(tan theta + mu)/(tan theta - mu) = (2 mu + mu)/(2mu - mu) = 3`