Question

At what angle the two Forces (F1+ F2 )and (F1- F2 ) act so that the resultant is √ 2(F1^2 +F2^2)​

Answer 1

Answer:

90°

Explanation:

  Resultant on vectors A and B is given by:

                 √A² + B² + 2ABcosθ , where θ is the angle between A and B.

Let (F₁ + F₂) and (F₁ - F₂) act at an angle of φ, then their resultant is:

⇒ √(F₁ + F₂)² + (F₁ - F₂)² + 2(F₁ + F₂)(F₁ - F₂)cosφ

⇒ √2(F₁² + F₂²) + 2(F₁² - F₂²)cosφ    

      Given that their resultant should be √2(F₁² + F₂²)

  Compare both the expressions:

⇒ √2(F₁² + F₂²) + 2(F₁² - F₂²)cosφ = √2(F₁² + F₂²)

⇒ 2(F₁² + F₂²) + 2(F₁² - F₂²)cosφ = 2(F₁² + F₂²)

⇒ 2(F₁² - F₂²)cosφ = 0

⇒ cosφ = 0   but 2(F₁² - F₂²) ≠ 0

⇒ cosφ = cos90°

⇒ φ = 90°

        They act at an angle of 90°

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Answer 2

Answer:

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• It acts at an angle of 90 degree.

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• Kindly refer the above given attachment for more information.
• And for better understanding.

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