A) \[a\]
B) \[a\sqrt{2}\]
C) \[a\sqrt{3}\]
D) \[2a\]
Correct Answer: C
Solution :
\[{{y}_{1}}=a\sin \left( \omega t+\frac{\pi }{6} \right)\] and \[{{y}_{2}}=a\cos \omega t=a\sin (\omega t+\lambda /2)\] \[\therefore \] \[R=\sqrt{a_{1}^{2}+a_{2}^{2}+2{{a}_{1}}{{a}_{2}}\cos ({{\phi }_{2}}-{{\phi }_{1}})}\] \[=\sqrt{{{a}^{2}}+{{a}^{2}}+2{{a}^{2}}\times \cos \left( \frac{\pi }{2}-\frac{\pi }{6} \right)}\] \[=\sqrt{2{{a}^{2}}+2{{a}^{2}}\times \frac{1}{2}}\] \[R=\sqrt{3a}\]
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