A) \[{{\tan }^{-1}}\left( \frac{\rho -\delta }{\rho +\delta } \right)\]
B) \[{{\tan }^{-1}}\left( \frac{\rho }{\delta } \right)\]
C) \[{{\tan }^{-1}}\left( \frac{\delta }{\rho } \right)\]
D) \[{{\tan }^{-1}}\left( \frac{\rho +\delta }{\rho -\delta } \right)\]
Correct Answer: A
Solution :
From the figure, we have \[\delta gR(cos\theta +sin\theta )=\rho gR(cos\theta -sin\theta )\] \[\Rightarrow \] \[\delta \cos \theta +\delta \sin \theta =\rho \cos \theta -\rho \sin \theta \] \[\Rightarrow \] \[\sin \theta (\delta +\rho )=cos\theta (\rho -\delta )\] \[\Rightarrow \] \[\tan \theta =\frac{\rho -\delta }{\rho +\delta }\]You need to login to perform this action.
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