Laws Of Motion Question 76
Question: Two forces with equal magnitudes F act on a body and the magnitude of the resultant force is F/3. The angle between the two forces is [MP PMT 1999]
Options:
A) $ {{\cos }^{-1}}( -\frac{17}{18} ) $
B) $ {{\cos }^{-1}}( -\frac{1}{3} ) $
C) $ {{\cos }^{-1}}( \frac{2}{3} ) $
D) $ {{\cos }^{-1}}( \frac{8}{9} ) $
Show Answer
Answer:
Correct Answer: A
Solution:
$ F _{ _{net}}^{2}=F _{1}^{2}+F _{2}^{2}+2F _{1}F _{2}\cos \theta $
therefore $ {{( \frac{F}{3} )}^{2}} $
$ =F^{2}+F^{2}+2F^{2}\cos \theta $
therefore $ \cos \theta =( -\frac{17}{18} ) $
