A) \[36.8{}^\circ \]
B) \[45{}^\circ \]
C) \[30{}^\circ \]
D) \[42.6{}^\circ \]
Correct Answer: A
Solution :
Retardation in upward motion \[=g(\sin \theta +\mu \cos \theta )\] \[\therefore \]Force required just to move up \[{{F}_{up}}=mg(\sin \theta +\mu \cos \theta )\] Similarly for down ward motion a \[=g(\sin \theta -\mu \cos \theta )\] \[\therefore \] Force required just to prevent the body sliding down \[{{F}_{dn}}=mg(\sin \theta -\mu \cos \theta )\] According to problem \[{{F}_{up}}=2{{F}_{dn}}\] Þ\[mg(\sin \theta +\mu \cos \theta )=2mg(\sin \theta -\mu \cos \theta )\] Þ\[\sin \theta +\mu \ \cos \theta =2\sin \theta -2\mu \ \cos \theta \] Þ\[3\mu \cos \theta =\sin \theta \]Þ \[\tan \theta =3\mu \] Þ\[\theta ={{\tan }^{-1}}(3\mu )={{\tan }^{-1}}(3\times 0.25)={{\tan }^{-1}}(0.75)\]\[=36.8{}^\circ \]
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