two forces f1 ,f2 are acting ata point, having resultant f. if f2 is doubled, f is also. doubled, if f2. is re veres then also f is doubled, thenf1:f2:f is
Answers
Answer:
F₁ : F₂ : F = (1/√3) : 1/2 : (1/√3)
Explanation:
Two forces F1 and F2 are acting at a point having resultant F if F2 is doubled F is also doubled if F2 is reversed then also F is doubled then
F² = F₁² + F₂² + 2F₁F₂Cosθ - eq 1
θ = Angle between F₁ & F₂
if F2 is doubled F is also doubled
(2F)² = F₁² + (2F₂)² + 2F₁(2F₂)Cosθ
4F² = F₁² + 4F₂² + 4F₁F₂Cosθ - eq2
F2 is reversed then also F is doubled
(2F)² = F₁² + (-F₂)² + 2F₁(-F₂)Cosθ
4F² = F₁² + F₂² - 2F₁F₂Cosθ - eq 3
Adding eq 1 & eq 3
5F² = 2F₁² + 2F₂²
Equating 2 & 3
F₁² + 4F₂² + 4F₁F₂Cosθ = F₁² + F₂² - 2F₁F₂Cosθ
=> 3F₂² = -6F₁F₂Cosθ
=> F₂ = -2F₁Cosθ
=> Cosθ = -F₂/2F₁
putting these values in equations
F² = F₁² + F₂² + 2F₁F₂( -F₂/2F₁)
F² = F₁²
F = F₁
5F² = 2F₁² + 2F₂²
=> 5F₁² = 2F₁² + 2F₂²
=> 3F₁² = 2F₂²
=> √3 F₁ = √2 F₂
=> F₁ = √2/√3 F₂
F = F₁ = 2/√3 F₂
=> √3F = √3F₁ = 2F₂
=> √3F₁ = 2F₂ = √3F
F₁ : F₂ : F = (1/√3) : 1/2 : (1/√3)
Explanation:
Then F1:F2:F is 1/√3:1/2:1/√3
