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Q.

Two horizontal forces of magnitudes 10 N & P N act on a particle. The force of magnitude 10 N acts due west & the force of magnitude P N acts on a hearing of $30^{0}$ east of north as shown in figure. The resultant of these two force acts due north. Find the magnitude of this resultant.

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a

$12 \sqrt{5} N$

b

$15 \sqrt{3}$

c

$10 \sqrt{2} N$

d

$10 \sqrt{3} N$

answer is D.

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Detailed Solution

Resultant acts along y-axis

$\Rightarrow P_{x} = P \cos 60^{0} = 10 N or \frac{P}{2} = 10 or P = 20$

$Resultant P_{y} = P \sin 60^{0} = 20 \times \frac{\sqrt{3}}{2} = 10 \sqrt{3} N$

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Two horizontal forces of magnitudes 10 N & P N act on a particle. The force of magnitude 10 N acts due west & the force of magnitude P N acts on a hearing of 300 east of north as shown in figure. The resultant of these two force acts due north. Find the magnitude of this resultant.