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AP EAMCET · PHYSICS · Mathematics in Physics

Two forces whose magnitudes are in the ratio \(5: 3\) are acting at a point at an angle \(60^{\circ}\) simultaneously. If the resultant of the two forces is \(35 \mathrm{~N}\), then the magnitudes of two forces respectively are

  1. A \(3 \mathrm{~N}, 5 \mathrm{~N}\)
  2. B \(25 \mathrm{~N}, 9 \mathrm{~N}\)
  3. C \(25 \mathrm{~N}, 15 \mathrm{~N}\)
  4. D \(12 \mathrm{~N}, 20 \mathrm{~N}\)
Verified Solution

Answer & Solution

Correct Answer

(C) \(25 \mathrm{~N}, 15 \mathrm{~N}\)

Step-by-step Solution

Detailed explanation

\begin{aligned} \frac{F_1}{F_2} & =\frac{5}{3} \\ F_1 & =\frac{5}{3} F_2 \\ F_{n e t} & =35 \\ F_{\text {net }} & =\sqrt{F_1^2+F_2^2+2 F_1 F_2 \cos \theta} \\ 35 & =\sqrt{\left(\frac{5}{3} F_2\right)^2+F_2^2+2 \times \frac{5}{3} F_2^2 \cos 60} \\ (35) & =\sqrt{\frac{25}{9}…