A) \[37{}^\circ \]
B) \[45{}^\circ \]
C) \[30{}^\circ \]
D) \[~53{}^\circ \]
Correct Answer: A
Solution :
[a] 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 downward 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 \[{{F}_{up}}=2{{F}_{dn}}\] \[\Rightarrow mg(sin\theta +\mu cos\theta )=2mg(sin\theta -\mu cos\theta )\] \[\Rightarrow \sin \theta +\mu cos\theta =2sin\theta -2\mu cos\theta \] \[\Rightarrow 3\mu \cos \theta =\sin \theta \Rightarrow \tan \theta =3\mu \] \[\Rightarrow \theta ={{\tan }^{-1}}(3\mu )=ta{{n}^{-1}}(3\times 0.25)=ta{{n}^{-1}}(0.75)=37{}^\circ \]
You need to login to perform this action.
You will be redirected in
3 sec
