Question

A body of mass $ m $ is at rest on a rough inclined plane having angle of inclination $ \theta $ with the horizontal, $ \mu $ is the coefficient of friction between the body and the plane. Then the minimum force needed to move the body up along the inclined plane is

• A. $ mg(sin\theta-\mu cos \theta) $
• B. $ mg(cos\theta-\mu sin \theta) $
• C. $ mg(cos\theta+ \mu sin \theta) $
• D. $ mg(sin\theta+ \mu cos \theta) $

Answer 1

Answer: (D)

The various forces acting on the body are shown in figure

The minimum force needed to move the body up along the Inclined plane is
$F=mgsin \theta+f =mgs\,in \theta+\mu N $
$=mgsin\theta+\mu mgcos\theta \left(as N=mgcos\theta\right)$
$=mg\left(sin\theta+\mu cos\theta\right)$