Question

At what angle the two equal forces should exert on a particle simultaneously so that resultant force is equal to either of the two forces?

• A. ${120}^o$
• B. ${90}^o$
• C. ${60}^o$
• D. ${180}^o$

Answer 1

Answer: (A)

${120}^o$

Let $\theta$ be the angle between the two vectors A and B such that, |A| = |B|.

Therefore,

R² = A² + B² + 2AB cos $\theta$

=> A² = A² + A² + 2(A)(A) cos $\theta$ [since, |A| = |B| = |R|]

=> A² = 2A² + 2A² cos $\theta$

=> cos $\theta$ = -1/2

=> $\theta$ = 120°