Question

The minimum force required to start pushing a body up a rough (Friction 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 $\theta =2\mu$ then the ratio $\frac{F_1}{F_2}$ is:

• A. $1$
• B. $2$
• C. $3$
• D. $4$

Answer 1

The correct option is C $3$

The minimum force required to start pushing a body on rough incline plane is

=component of weight along down the incline+ friction

$F_1=mgsin\theta +\mu mgcos\theta$

Minimum force to prevent sliding on rough inclined plane

$F_2=mgsin\theta -\mu mgcos\theta$

$\frac{F_1}{F_2}=\frac{tan\theta +\mu }{tan\theta -\mu }$

$\frac{F_1}{F_2}=3$