KVPY Sample Paper KVPY Stream-SX Model Paper-28

Two forces P and Q, of magnitude 2F and 3F, respectively, are at an angle \[\theta \] with each other. If the force Q is doubled, then their resultant also gets doubled. Then, the angle \[\theta \] is:

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

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

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

D) \[30{}^\circ \]

Correct Answer: A

Solution :

\[2|\overrightarrow{P}+\overrightarrow{Q}|=|\overrightarrow{P}+2\overrightarrow{Q}|\] \[\Rightarrow \] \[13+12\cos \theta =10+6\cos \theta \]

\[\cos =-\frac{1}{2}\]

\[\theta =120{}^\circ .\]