Two equal forces act on a body. It is found that the square of their resultant is twice the square of each force acting on it, then find the least angle between the two forces (in degrees).
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Resultant = A 2 + B 2 + 2 A B cos θ
Let the two forces be x ,
Then according to the given conditions:-
x 2 + x 2 + 2 × x × x cos θ = 2 F 2 2 x 2 + 2 x 2 cos θ = 2 F 2 2 x 2 ( 1 + cos θ ) = 2 F 2 1 + cos θ = 1 cos θ = 0 ∴ θ = 9 0 ° ( or ) 2 7 0 °
So, the least angle is 9 0 ° .