Question

The force required to just move a body up an inclined plane is double the force required to just prevent it from sliding down. If $\theta$ is the angle of friction and $\varphi$ is the angle which the plane makes with horizontal, then:

• A. $tan\varphi =2tan\theta$
• B. $tan\varphi =3tan\theta$
• C. $tan\varphi =tan\theta$
• D. $tan\theta =3tan\varphi$

Answer 1

The correct option is B $tan\varphi =3tan\theta$



Force required to just move up the body = $F_{up}=mgsin\varphi +\mu mgcos\varphi$ similarly
$F_{down}=mgsin\varphi -\mu mgcos\varphi F_{up}=2F_{down}mgsin\varphi +\mu mgcos\varphi =2(mgsin\varphi -\mu mgcos\varphi )tan\varphi =3\mu$
As we known $\mu =tan\theta$
$\therefore tan\varphi =3tan\theta$