# A block is placed on a rough inclined plane of inclination $\theta=30 ^{\circ}$ . If the force to drag it along the plane is to be smaller than to lift it, the coefficient of friction $\mu$ should be less than

$(a)\;\frac{1}{2}\quad (b)\;\frac{\sqrt 3}{2} \quad (c)\;\frac{2}{3} \quad (d)\;\frac{1}{\sqrt 3}$

Let mass be m. The required to lift it is $F_2=mg$
$F_1$=force required to drag it along the plane
$f_1=mg \sin \theta+\mu mg \cos \theta$
$F_1 < F_2$
$mg \sin \theta +\mu mg \cos \theta < mg$
$\mu < \large\frac{1- \sin \theta}{\cos \theta}$
$\mu < \large\frac{1- \sin 30}{\cos 30}$
$\mu < \large\frac{1}{\sqrt 3}$
Hence d is the correct answer.

edited Jan 26, 2014 by meena.p