Question

7. One of the two forces is double and the other resultant is
equal to the greater force. The angle between them is
​

Answer 1

Answer :

• The angle between the two forces will be cos⁻¹ (1/4) .

Explanation :

Given that,

• one of the two forces is double and the other resultant is equal to the greater force

so,

Let magnitude of smaller force , F₁ = F

then, magnitude of greater force F₂ = 2 F

and, magnitude of Resultant of of two forces, R = 2 F

Let, the angle between F₁ and F₂ be θ

then, Using the formula for magnitude of Resultant of two vectors

• R² = A² + B² + 2 A B cos θ

[ where R is the magnitude of resultant of two vectors with magnitude A and B and θ is the angle between vectors A and B ]

so,

→ R² = F₁² + F₂² + 2 F₁ F₂ cos θ

→ (2F)² =  (F)² + (2F)² + 2 (F) (2F) cos θ

→ 4 F² = F² + 4 F² + 4 F² cos θ

→ 4 F² - 4 F² = F² + 4 F² cos θ

→ 0 = F² ( 1 - 4 cos θ )

→ 0 = 1 - 4 cos θ

→ 1 = 4 cos θ

→ cos θ = 1 / 4

→ θ = cos⁻¹ ( 1/4 )

therefore,

• The angle between the two forces will be cos⁻¹ (1/4) .