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

JEE · Physics · previous-year question

  1. A.$$\frac{5 A}{2}$$
  2. B.$$\frac{\sqrt{5} A}{4}$$
  3. C.$$\frac{\sqrt{5} A}{2}$$correct
  4. D.$$\frac{\sqrt{5} A^{2}}{2}$$

Answer

C. $$\frac{\sqrt{5} A}{2}$$

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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