How is the resultant force calculated if two forces act along the same straight line but in opposite directions?

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RRB JE ME 22 Apr 2025 Shift 2 CBT 2 Official Paper
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  1. R=F1+F2
  2. \(R=\sqrt{F_{1}^{2} + F_{2}^{2} } \)
  3. \(R=2F_1F_2cos\theta\)
  4. \(R=F_1 - F_2\)

Answer (Detailed Solution Below)

Option 4 : \(R=F_1 - F_2\)
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Detailed Solution

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Concept:

When two forces act along the same straight line but in opposite directions, the resultant force is determined by their algebraic sum, considering their directions.

Given:

  • Force 1, \( F_1 \) (acting in the positive direction)
  • Force 2, \( F_2 \) (acting in the negative direction)

Step 1: Assign Directions

Assume \( F_1 \) is positive (e.g., rightward) and \( F_2 \) is negative (e.g., leftward).

Step 2: Calculate Resultant Force

The resultant force \( R \) is the sum of the two forces, accounting for their directions:

\( R = F_1 - F_2 \)

 
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