If the resultant of two equal forces is `sqrt(3)` times a single . force, find the angle between the forces .

Explanation

Two two forces are equal (i.e.,)
P = Q
Here R `= sqrt(3P)`
`R = sqrt(P^(2) +Q^(2) + 2P Q cos theta)`
Substituting the values
`sqrt(3P) = sqrt(P^(2) + P^(2) + 2P^(2) cos theta)`
Squaring both sides
`3P^(2) + P^(2) + P^(2) + 2P^(2) cos theta`
`3P^(2) = P^(2) (1 + 1+ 2cos theta)`
`= 2P^(2) + 2P^(2) cos theta`
`:. P^(2) = 2P^(2) cos theta`
`2 cos theta = 1`
`cos theta = (1)/(2) (or) theta = 60^(@)` .