A) \[\frac{1}{4}\left( \frac{\sqrt{3}}{2} \right)\]
B) \[\frac{1}{4}-\frac{\sqrt{3}}{2}\]
C) \[\frac{1}{2\sqrt{3}}\]
D) \[2\sqrt{3}\]
Correct Answer: C
Solution :
Acceleration is given by as \[a=g\sin \theta -\mu \,\,g\,\,\cos \theta \] or \[\frac{g}{4}=g(\sin \theta -\mu \,\,\cos \theta )\] or \[\frac{1}{4}=(\sin {{30}^{o}}-\mu \,\,\cos \,\,{{30}^{o}})\] or \[\frac{1}{4}=\frac{1}{2}-\frac{\mu \sqrt{3}}{2}\] or \[\frac{\mu \sqrt{3}}{2}=\frac{1}{2}-\frac{1}{4}=\frac{1}{4}\] \[\mu =\frac{1}{2\sqrt{3}}\]
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