A) \[\frac{1}{2}\]
B) \[\frac{3}{4}\]
C) \[\frac{2}{3}\]
D) \[\frac{1}{4}\]
Correct Answer: A
Solution :
The figure shows free body diagram of the block. For equilibrium, along the plane \[\mu R+T\cos {{45}^{o}}=mg\sin {{45}^{o}}\] \[\mu R+T\frac{1}{\sqrt{2}}=\frac{mg}{\sqrt{2}}\] (i) For equilibrium, in direction \[\bot \]to inclined plane,\[R=T\sin {{45}^{o}}+mg\cos {{45}^{o}}\] \[=\frac{T}{\sqrt{2}}+\frac{mg}{\sqrt{2}}\] Put this value of R in (i), \[\frac{\mu }{2}(T+mg)=\frac{1}{\sqrt{2}}(mg-T)\] \[\mu (50+15\times 10)=(15\times 10-50)\] \[\mu =\frac{100}{200}=\frac{1}{2}\] Hence, the correction option is (a).You need to login to perform this action.
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