Two forces F ⃗ 1 \vec{F}_1 F 1 and F ⃗ 2 \vec{F}_2 F 2 are acting on a body. One force has magnitude thrice that of the other force and the resultant of the two forces is equal to the force of larger magnitude. The angle between F₁ and F₂ is cos⁻¹(1/n). The value of |n| i s ____.
Physics · Mathematical tools and vector
JEE Mains 2024 04 Apr Morning Shift

Question

Two forces F ⃗ 1 \vec{F}_1 F 1 ​ and F ⃗ 2 \vec{F}_2 F 2 ​ are acting on a body. One force has magnitude thrice that of the other force and the resultant of the two forces is equal to the force of larger magnitude. The angle between F₁ and F₂ is cos⁻¹(1/n). The value of |n| i s ____.

G1 Physics · Accepted Answer

Let: |F⃗₁| = F |F⃗₂| = 3F and resultant magnitude: R = 3F Using: R² = F₁² + F₂² + 2F₁F₂ cosθ 9F² = F² + 9F² + 6F² cosθ 6F² cosθ = -F² cosθ = -1/6 Given: θ = cos⁻¹(1/n) Therefore: 1/n = -1/6 n = -6 Hence: |n| = 6

Two forces F ⃗ 1 \vec{F}_1 F 1 ​ and F ⃗ 2 \vec{F}_2 F 2 ​ are acting on a body. One force has magnitude thrice that of the other force and the resultant of the two forces is equal to the force of larger magnitude. The angle between F₁ and F₂ is cos⁻¹(1/n). The value of |n| i s ____.

Two forces F ⃗ 1 \vec{F}_1 F 1 and F ⃗ 2 \vec{F}_2 F 2 are acting on a body. One force has magnitude thrice that of the other force and the resultant of the two forces is equal to the force of larger magnitude. The angle between F₁ and F₂ is cos⁻¹(1/n). The value of |n| i s ____.