Physics Vectors & Equilibrium PMDC Conceptual Practice
PMDC Verified Question 18 of 50
The magnitude of the resultant of two forces is at its minimum value when the angle between them is:
A
\(0^\circ\)
B
\(45^\circ\)
C
\(90^\circ\)
D
\(180^\circ\)
Tap any option to test your recall and reveal the step-by-step Propolis autopsy.

Propolis Cognitive Error Autopsy

Official Correct Choice:
Option D: \(180^\circ\)
Concept:
Law of cosines for vector addition and its extrema.

Formula:
$$R = \sqrt{F_1^2 + F_2^2 + 2F_1F_2\cos\theta}$$

Solution:
To minimize \(R\), we need to minimize \(\cos\theta\). The minimum value of the cosine function is \(-1\), which occurs when:
$$\theta = 180^\circ$$
In this case:
$$R = \sqrt{F_1^2 + F_2^2 - 2F_1F_2} = \sqrt{(F_1 - F_2)^2} = |F_1 - F_2|$$
This matches the scenario where the forces point in opposite directions.

Why other options are incorrect:
  • \(0^\circ\) yields the maximum possible resultant (\(F_1 + F_2\)).
  • \(90^\circ\) yields \(\sqrt{F_1^2 + F_2^2}\), which is greater than the minimum difference.
  • \(45^\circ\) yields an intermediate value.

Quality & Fidelity Assurance: Every question on BeambePrep is rigorously curated against the official PMDC syllabus with zero filler, zero out-of-syllabus content, and zero typos. When an authentic past paper originally contained a historical mistake or ambiguity from the examining board (such as UHS or NUMS), BeambePrep faithfully reflects the original paper while detailing the nuance and scientific consensus in the autopsy above.

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