Two forces of equal magnitude (= Q) act at an angle of θ to each other. The resultant of these forces will be:

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Question

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JSSC JE Mechanical Re-Exam 23 Oct 2022 Official Paper-II

Answer 1

Explanation:

When two equal forces (=Q) make an angle θ, the resultant (R) of the two forces is given by:

\(R=\sqrt{F_1^2+F_2^2+2F_1F_2\cosθ}\;\)

Since the two forces are equal; and \(F_1=F_2=Q\)

\(R=\sqrt{Q_1^2+Q_2^2+2Q_1Q_2\cosθ}\;\)

\(R=\sqrt{Q^2+Q^2+2Q^2\cosθ}\;\)

\(R=\sqrt{2Q^2+2Q^2\cosθ}\;\)

\(R=\sqrt{2Q^2(1\;+\;\cosθ)}\;\)

We know that;

1 + cos θ = 2 cos2(θ/2)

\(R=\sqrt{2Q^2[2\cos^2(θ/2)]}\;\)

\(\therefore R= 2\ Q \cos \frac{\theta}{2}\)