Two forces having magnitude A and are perpendicular to each other. The magnitude of their resultant is [2023]

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Solution

Q.
Two forces having magnitude A and $\frac{A}{2}$ are perpendicular to each other. The magnitude of their resultant is [2023]

1 $\frac{\sqrt{5} A}{4}$

2 $\frac{5 A}{2}$

3 $\frac{\sqrt{5} A^{2}}{2}$

4 $\frac{\sqrt{5} A}{2}$

Ans.
(4)

$\vec{F} = ({\vec{F}}_{1} + {\vec{F}}_{2})$

$| \vec{F} |$ $= \sqrt{F_{1}^{2} + F_{2}^{2} + 2 F_{1} F_{2} \cos 90 °}$

$= \sqrt{A^{2} + \frac{A^{2}}{4}} = \frac{A \sqrt{5}}{2}$

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