A) \[\frac{1}{2}\]
B) \[\frac{\sqrt{3}}{2}\]
C) \[\frac{\sqrt{3}}{4}\]
D) \[\frac{2}{3}\]
Correct Answer: B
Solution :
Case I. When 2 N force is acting on the block resolve the forces along and perpendicular the plane. \[-2=mg\sin \theta -\mu mg\,\cos \theta \] ...(i) Case II. When the force 10 N is acting on the block, free body diagram of the block is given as follow: \[mg\sin \theta +\mu mg\,\cos \theta =10\] ...(ii) Dividing eq. (i) by eq. (ii), \[\frac{g\sin \theta -\mu g\,\cos \theta }{g\sin \theta +\mu g\,\cos \theta }=\frac{-2}{10};\frac{1-\mu \sqrt{3}}{1+\mu \sqrt{3}}=\frac{-1}{5}\Rightarrow \mu =\frac{\sqrt{3}}{2}\]cYou need to login to perform this action.
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