If two forces act at a right angle (90°), what will be the magnitude of their resultant force?

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RRB JE ME 22 Apr 2025 Shift 1 CBT 2 Official Paper
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  1. \(R = \sqrt{F_1^2 + F_ 2^2}\)
  2. \(R = F_1 - F_2\)
  3. \(R = 2F_1F_2\cos\theta\)
  4. \(R = F_1 + F_2\)

Answer (Detailed Solution Below)

Option 1 : \(R = \sqrt{F_1^2 + F_ 2^2}\)
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Detailed Solution

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Concept:

When two forces act at a right angle (90°), their resultant is found using vector addition based on the Pythagorean theorem.

If:

  • Force 1 = F1
  • Force 2 = F2
  • Angle between them = 90°

Resultant force formula:

\( R = \sqrt{F_1^2 + F_2^2} \)

This formula gives the magnitude of the resultant of two perpendicular vectors.

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