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
$F=mgsin\theta +f=mgsin\theta +\mu N$
$=mgsin\theta +\mu mgcos\theta \left(asN=mgcos\theta \right)$
$=mg\left(sin\theta +\mu cos\theta \right)$