JEE MAIN - Physics (2023 - 8th April Morning Shift - No. 9)
Two forces having magnitude $$A$$ and $$\frac{A}{2}$$ are perpendicular to each other. The magnitude of their resultant is:
$$\frac{5 A}{2}$$
$$\frac{\sqrt{5} A}{4}$$
$$\frac{\sqrt{5} A}{2}$$
$$\frac{\sqrt{5} A^{2}}{2}$$
Explanation
The resultant of two perpendicular vectors is given by the Pythagorean theorem.
If we have two vectors of magnitudes $A$ and $\frac{A}{2}$, the resultant $R$ is:
$R = \sqrt{A^{2} + \left(\frac{A}{2}\right)^{2}} = \sqrt{A^{2} + \frac{A^{2}}{4}} = \sqrt{\frac{5A^{2}}{4}} = \frac{\sqrt{5} A}{2}$.
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