Two equal forces of 10 N each act at 90° to each other. The resultant is:
A0 N
B10 N
C10√2 NCORRECT
D20 N
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Why the answer is C, and why the others tempt you.
**The reasoning**
When two forces act at 90° (perpendicular), we can't just add them directly — we use **vector addition**. Picture a right-angled triangle: one force points right (10 N), the other points up (10 N). The resultant is the hypotenuse.
Using Pythagoras' theorem:
R² = F₁² + F₂²
R² = 10² + 10²
R² = 100 + 100 = 200
R = √200 = √(100 × 2) = 10√2 N ≈ 14.14 N
**Why the wrong options tempt you**
- **0 N** — You might think equal forces cancel out, but that only happens when they act in *opposite* directions (180°), not at 90°.
- **10 N** — Tempting if you assume the forces "balance" somehow, but perpendicular forces don't cancel.
- **20 N** — This is if you just add them arithmetically (10 + 10), forgetting that forces are vectors with direction, not simple numbers.
**Quick takeaway**
When forces meet at 90°, think Pythagoras! The resultant is always larger than either individual force but smaller than their sum — specifically, it's the hypotenuse of your force triangle.
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