1.

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

Answer»

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°


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