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Q56 (NDA-I/2023) Science & Technology › Basic Science (Physics, Chemistry, Biology) Official Key

Two forces of 5.0 N each are acting on a point mass. If the angle between the forces is 60°, then the net force acting on the point mass has magnitude close to :

Explanation

The magnitude of the net force (resultant force) acting on a point mass when two forces P and Q act at an angle θ is determined using the law of cosines for vector addition:

R = √(P² + Q² + 2PQ cos θ)

Given the values:

  • Force P = 5.0 N
  • Force Q = 5.0 N
  • Angle θ = 60°

Substituting these into the formula, and knowing that cos 60° = 0.5:

R = √(5.0² + 5.0² + 2 × 5.0 × 5.0 × 0.5)
R = √(25 + 25 + 25)
R = √75

The value of √75 is approximately 8.66 N. Therefore, the magnitude of the net force acting on the point mass is closest to 8.6 N, making Option A the correct choice.

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