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NEET Sample Paper NEET Sample Test Paper-17

  • question_answer
    If two SHMs are represented by equations \[{{y}_{1}}=10\]\[\sin (3\pi t+\pi /4)\] and \[{{y}_{2}}=5[\sin (3\pi t)+\]\[\sqrt{3}\cos (3\pi t)]\]the ratio of their amplitudes is:

    A)  2 : 1                           

    B)  1 : 2                           

    C)  1 : 1                   

    D)    \[1:\sqrt{2}\]

    Correct Answer: C

    Solution :

    \[{{y}_{1}}=10\sin \left( 3\pi t+\frac{\pi }{4} \right)\] \[{{y}_{2}}=10\left[ \frac{1}{2}\sin 3\pi t+\frac{\sqrt{3}}{2}\cos 3\pi t \right]\] \[=10[cos{{60}^{o}}sin3\pi t+sin{{60}^{o}}cos3\pi t]\] \[=10[\sin ({{60}^{o}}+3\pi t)]\] \[=10\sin (3\pi t+{{60}^{o}})\] \[\therefore \]ratio of amplitudes \[=1:1\] Hence, the correction option is [c].


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