Question

The resultant of two forces, one double the other in magnitude is perpendicular to the smaller of the
two forces. The angle between the two forces is
(1) 150
(2) 90°
(3) 60°
(4) 120°
Find the resultant of three vectors OA. OB and OC shown in the following fiqura Radine of the​

Answer 1

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° and therefore the answer is option (4)

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Answer 2

Answer:

A)120

Explanation:

First we need to find out resultant... That comes out to be root 3 times smaller side.... Then by applying sinx = perpendicular /hypotnuse...= root 3/2... We get x = 60.....which is b/w smaller and - ve of larger angle.... To make it positive we invert it.. So angle becomes 180