OnlineCBT
Physics · MOTION IN A PLANE
हिन्दीThree coplanar forces \( \mathbf{F}_1 \), \( \mathbf{F}_2 \), and \( \mathbf{F}_3 \) keep a body in static equilibrium. If \( |\mathbf{F}_1| = 5\text{ N} \), \( |\mathbf{F}_2| = 12\text{ N} \), and \( |\mathbf{F}_3| = 13\text{ N} \), what is the angle between the forces \( \mathbf{F}_1 \) and \( \mathbf{F}_2 \)?
Correct answer · Option 4
\( \pi/2\text{ rad} \)
Explanation
Equilibrium implies \( \mathbf{F}_1 + \mathbf{F}_2 = -\mathbf{F}_3 \implies F_1^2 + F_2^2 + 2F_1F_2\cos\theta = F_3^2 \implies 5^2 + 12^2 + 2(5)(12)\cos\theta = 13^2 \implies 169 + 120\cos\theta = 169 \implies \cos\theta = 0 \implies \theta = \pi/2\text{ rad} \).
