question_answer

A particle of weight \[W\]rests on a rough inclined plane which makes an angle \[\alpha \] with the horizontal. If the coefficient of static friction \[\mu =2\] tan a, find the horizontal force \[H\] acting transverse to the slope of the plane when the particle is about to slip.

A) \[2W\,\sin \alpha \]        

B) \[W\,\sin \,\alpha \]

C) \[\frac{\sqrt{3}}{2}W\,\sin \,\alpha \]     

D) \[W\sqrt{3}\,\sin \,\alpha \]

Correct Answer: D

Solution :

[d] Net force: \[F=\sqrt{{{(Wsin\alpha )}^{2}}+{{H}^{2}}}\] When the particle is about to slip: \[F=\mu N\] \[\Rightarrow \sqrt{{{(Wsin\alpha )}^{2}}+{{H}^{2}}}=(2tan\alpha )Wcos\alpha \] \[\Rightarrow H=\sqrt{3}W\sin \alpha \]