A) \[\tan \,\theta \,\,\ge \,\,\mu \,\]
B) \[\cot \,\theta \,\,\ge \,\,\mu \,\]
C) \[\tan \,\,\frac{\theta }{2}\,\,\ge \,\,\mu \,\]
D) \[cot\,\,\frac{\theta }{2}\,\,\ge \,\,\mu \,\]
Correct Answer: D
Solution :
\[N\,\,=\,\,Mg\,\,-\,\,F\,cos\,\theta \] \[N\,\,=\,\,Mg\left( 1-cos\,\theta \right)\] \[f=\mu N\,\,=\mu Mg\,\left( 1-cos\,\theta \right)\] To move the block \[f\,\,\le \,\,F\,sin\,\theta \] \[\mu Mg(1-cos\,\theta )\,\le \,Mgsin\theta \] \[\mu \,\,\le \,\,\frac{\sin \,\theta }{1-\,\cos \,\theta }\] \[\mu \,\,\le \,\,\frac{2\,\sin \,\frac{\theta }{2}\,\cos \,\frac{\theta }{2}}{2\,{{\sin }^{2}}\frac{\theta }{2}}\] \[\mu \,\,\le \,\,\cot \,\frac{\theta }{2}\]You need to login to perform this action.
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