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Two forces, with equal magnitude F, act ...

Two forces, with equal magnitude F, act on a body and the magnitude of the resultant force is `F/3`. The angle between the two forces is:

A

`cos^(-1)(-17/18)`

B

`cos^(-1)(-1/3)`

C

`cos^(-1) (2/3)`

D

`cos^(-1) (8/9)`

Text Solution

Verified by Experts

The correct Answer is:
a
Resultant of two vectors a and B, which are working at an angle `theta`, can be given by:
`R = sqrt(A^(2) + B^(2) + 2A.B cos theta)` [As A= B =F and `R = F/3`]
`(F/3)^(2) =F^(2) +F^(2) + 2F^(2) cos theta`
`F^(2)/9 = 2F^(2) + 2F^(2) cos theta`
`rArr -17/9 F^(2) =2F^(2) cos theta`
`rArr cos theta =(-17/18)` or `theta = cos^(-1) (-17/18)`
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