Two forces of 5.0 N each are acting on a point mass. If the angle betw

Two forces of 5.0 N each are acting on a point mass. If the angle between the forces is 60°, then the net force acting on the point mass has magnitude close to :

8.6 N
4.3 N
5.0 N
6.7 N
This question was previously asked in
UPSC NDA-1 – 2023
The correct option is A.
The magnitude of the resultant of two vectors (forces) can be found using the formula derived from the law of cosines: $|R| = \sqrt{|F_1|^2 + |F_2|^2 + 2|F_1||F_2|\cos\theta}$, where $\theta$ is the angle between the forces.
Given $|F_1| = 5.0$ N, $|F_2| = 5.0$ N, and $\theta = 60°$. The magnitude of the resultant force is $|R| = \sqrt{5.0^2 + 5.0^2 + 2 \cdot 5.0 \cdot 5.0 \cdot \cos(60°)}$.
$|R| = \sqrt{25 + 25 + 2 \cdot 25 \cdot (1/2)} = \sqrt{50 + 25} = \sqrt{75}$.
$\sqrt{75} = \sqrt{25 \cdot 3} = 5\sqrt{3}$.
Using the approximation $\sqrt{3} \approx 1.732$, $|R| \approx 5 \times 1.732 = 8.66$.
The closest value among the options is 8.6 N.
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