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     [KCET 2002]

A)             \[{{60}^{\text{o}}}\]

B)           \[{{120}^{\text{o}}}\]

C)             \[{{150}^{\text{o}}}\]        

D)             \[{{90}^{\text{o}}}\]

Correct Answer: B

Solution :

                \[\tan \alpha =\frac{2F\sin \theta }{F+2F\cos \theta }=\infty \](as\[\alpha =\text{ }90{}^\circ \])             Þ\[F+2F\cos \theta =0\]             Þ\[\cos \theta =-\frac{1}{2}\]             \[\theta =120{}^\circ \]