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Q57 (CDS-II/2026) Science & Technology › Basic Science (Physics, Chemistry, Biology)

Two parallel, but not necessarily unidirectional, forces of magnitude 1 N and 2 N are acting on a body. Two more, parallel, again not necessarily unidirectional, forces of magnitude 3 N and 1 N, but perpendicular to the earlier forces, are applied to the body. Which one among the following are the smallest and largest possible magnitudes of the resultant force on the body ?

Result
Your answer: —  ·  Correct: C

Explanation

The resultant of two parallel forces F1 and F2 depends on their relative direction: it is either |F1 + F2| (if unidirectional) or |F1 - F2| (if opposite).

  • For the first set (1 N and 2 N), the possible resultants (R1) are 1 N (2 - 1) or 3 N (2 + 1).
  • For the second set (3 N and 1 N), the possible resultants (R2) are 2 N (3 - 1) or 4 N (3 + 1).

Since the two sets are perpendicular to each other, the total resultant magnitude R is calculated using the Pythagorean theorem: R = √(R12 + R22).

  • Minimum R: √(12 + 22) = √5 N
  • Maximum R: √(32 + 42) = √25 = 5 N

The other combinations (√17 N and √13 N) fall between these values. Thus, the smallest and largest magnitudes are √5 N and 5 N.

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