Question

Hey guys,

Two forces of magnitude F have a resultant of the same magnitude F.The angle b/w the two forces is

1)45degree
2)120degree
3)150degree
4)60 degree

if u know the answer then only answer it otherwise leave it.

Answer 1

Force is vector quantity . Resultant of two vectors A and B is given by

R = √{A² + B² + 2A.BcosФ} , where Ф is angle between A and B

Now, magnitude of each force is F and resutant is also F

Then, F = √{F² + F² + 2.F.FcosФ}

⇒F² = F² + F² + 2F².cosФ

⇒- F² = 2F²cosФ

⇒ -1/2 = cosФ

⇒cosФ = -1/2 = cos120°

⇒Ф = 120°

Hence angle between them is 120°