JEE Mains · Physics · STD 11 - 3.1 vectors
Two forces having magnitude \(A\) and \(\frac{ A }{2}\) are perpendicular to each other. The magnitude of their resultant is
- A \(\frac{\sqrt{5}\,A }{4}\)
- B \(\frac{5\,A }{2}\)
- C \(\frac{\sqrt{5}\,A ^2}{2}\)
- D \(\frac{\sqrt{5}\,A }{2}\)
Answer & Solution
Correct Answer
(D) \(\frac{\sqrt{5}\,A }{2}\)
Step-by-step Solution
Detailed explanation
\(\overrightarrow{ F }=\left(\overrightarrow{ F }_1+\overrightarrow{ F }_2\right)\) \(|\overrightarrow{ F }|=\sqrt{ F _1^2+ F _2^2+2 F _1 F _2 \cos 90^{\circ}}\) \(=\sqrt{ A ^2+\frac{ A ^2}{4}}=\frac{ A \sqrt{5}}{2}\)
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