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

Question

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

Answer 1

http://clay6.com/mpaimg/jee%203%2053.JPG

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.