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The resultant of two forces one double the other in magnitudes is perpendicular to the smaller of the two forces.The angle between the two forces is

The resultant of two forces one double the other in magnitudes is perpendicular to the smaller of the two forces.The angle between the two forces is

Grade:10

2 Answers

Arun
25750 Points
4 years ago
Let two forces F₁ and F₂ are given
A/C to question, 
|F₁| = 2|F₂|
Resultant of two forces F₁ and F₂ are given by 
R = F₁ + F₂ 
A/C to question, 
R is perpendicular upon smaller force.
Here smaller force is F₂.
So, R.F₂ = 0
⇒(F₁ + F₂).F₂ = 0
⇒F₁.F₂ + F₂² = 0 
⇒|F₁||F₂|cosФ + |F₂|² = 0 
Now, put |F₁| = 2|F₂| 
⇒2|F₂|.|F₂|cosФ + |F₂|² = 0
⇒2cosФ + 1 = 0 
⇒cosФ = -1/2 = cos120°
Hence, angle between two forces is 120°
 
Khimraj
3007 Points
4 years ago
Assume that F and 2F respectively
Let R be the Resultant .
It is given that R is perpendicular to F
Then
R^2+ F^2 = 4F^2
R^2 = 3F^2
3F^2-5F^2 = 4F^2cosα
-2F^2 = 4F^2cosα
Cosα = -1/2
α = 2π/3.

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