Question

THE MAGNITUDE OF THE RESULTANT OF TWO FORCES IS 2F. IF THE MAGNITUDE OF EACH FORCE IS F . THAN THE ANGLE BETWEEN THESE FORCES IS :-

Answer 1

cos theta = F+F /root(F^2 +F^2)
cos theta = 2F/root(2F^2)
cos theta =2F/root2 F
cos theta =2/root2
cos theta= root2
there is 0 degree angle because there is no value of root2 in cos theta.

Answer 2

We know that according to parallelogram law : The resultant of two forces F₁ and F₂ acting at a point with θ being the angle between those two forces is

R = Square root of F₁² + F₂² + 2 × F₁ × F₂ Cosθ

⇒ R² = F₁² + F₂² + 2 × F₁ × F₂ Cosθ

Given F₁ = F and F₂ = F and R = 2F

substituting the above values in the resultant equation we get :

⇒ 4F² = F² + F² + 2F² × Cosθ

⇒ 4F² = 2F² + 2F² × Cosθ

⇒ 4F² = 2F² (1 + Cosθ)

⇒ 2 = 1 + Cosθ

⇒ Cosθ = 1

we know that Cosθ = 1 when the θ = 0°

⇒ The angle between the two forces of magnitude F and Resultant 2F is 0°