Two forces of magnitude 8N and 4N act at right angle to each other. The angle between the resultant and the 8N force is

Analyze the question: Two perpendicular forces (8 N and 4 N) are combined. We need the angle between the resultant and the 8 N force.

Concept: When two forces act at right angles, the resultant is the diagonal of the rectangle formed by them. The angle θ between the resultant and one force is found using trigonometry:

• tan θ = (side opposite θ) / (side adjacent to θ)

For the angle with the 8 N force, the opposite side is the 4 N force and the adjacent side is the 8 N force.

Solution:

1. Resultant magnitude: R = √(8² + 4²) = √80 ≈ 8.94 N

2. Angle with the 8 N force: tan θ = 4/8 = 0.5 θ = tan⁻¹(0.5) ≈ 26.57° ≈ 26.6°

3. Check: cos θ = 8/8.94 = 0.894, and cos 26.6° ≈ 0.894. ✔

The angle with the 4 N force would be 90° − 26.6° = 63.4°, which is option E. This is the common trap, so read carefully which force the question asks about.

Answer: The angle between the resultant and the 8 N force is 26.6°, which is option B.

Tip: The resultant always lies closer to the larger force, so the angle with the larger force must be the smaller one (less than 45°). That lets you eliminate 60.0° and 63.4° immediately.