Two forces whose magnitudes are in the ratio 5: 3 are acting at a point at an angle 60° simultaneously. If the resultant of the two forces is 35 N, then the magnitudes of two forces respectively are

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12N, 20N

25N, 9N

25N, 15N

3N, 5N

answer is C.

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Detailed Solution

Let $F_{1} = 5 x$

$F_{2} = 3 x$

$F_{R} = 35, θ = 60 °$

$\Rightarrow F_{R}^{2} = F_{1}^{2} + F_{2}^{2} + 2 F_{1} F_{2} \cos θ$

$\Rightarrow {(35)}^{2} = {(3 x)}^{2} + {(5 x)}^{2} + 2 \times 3 x \times 5 x \times \cos 60 °$

$= 9 x^{2} + 25 x^{2} + 2 \times 15 x^{2} \times \frac{1}{2}$ $= 49 x^{2}$

$\Rightarrow 35 = 7 x$

$\Rightarrow x = \frac{35}{7} = 5$

$F_{1} = 3 x = 3 \times 5 = 25$

$F_{2} = 5 x = 5 \times 5 = 15$

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