question_answer

The resultant of two forces, one double the   other in magnitude, is perpendicular to the smaller of the two forces. The angle between the two forces is:

A) \[120{}^\circ \]

B) \[60{}^\circ \]

C) \[90{}^\circ \]

D) \[150{}^\circ \]

Correct Answer: A

Solution :

\[{{F}_{1}}=(F)\]one force \[{{F}_{2}}=(2F)\]second force Let \[\theta \] is angle between \[{{F}_{1}}\] and \[{{F}_{2}}.\] Here angle made by resultant \[{{F}_{R}}\]is \[\alpha \]with \[{{F}_{1}}\] \[\therefore \] \[\alpha =90\] \[\tan \alpha =\frac{{{F}_{2}}\sin \theta }{{{F}_{1}}+{{F}_{2}}\cos \theta }=\alpha \] \[\frac{{{F}_{2}}\sin \theta }{{{F}_{1}}+{{f}_{2}}\cos \theta }=\frac{1}{0}\] \[{{F}_{1}}+{{F}_{2}}\cos \theta =0\] \[2F\cos \theta =-F\] \[\cos \theta =-1/2\] \[\theta =120\]