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NEET Sample Paper NEET Sample Test Paper-22

  • question_answer
    The displacement of a particle varies according to the relation \[x=4(\cos \pi t+\sin \pi t)\]The amplitude of the particle is:

    A)  8                                

    B)  -4                   

    C)       4                    

    D)      \[4\sqrt{2}\]

    Correct Answer: D

    Solution :

    \[x=4(\cos \pi t+\sin \pi t)\] \[=4\sqrt{2}\left\{ \frac{1}{\sqrt{2}}\cos \pi t+\frac{1}{2}\sin \pi t \right\}\] \[=4\sqrt{2}\{\sin {{45}^{o}}{{C}_{\cos }}\pi t+\cos {{45}^{o}}\sin \pi t\}\] \[=4\sqrt{2}\{\sin (\pi t+{{45}^{o}})\}\] \[\therefore \]\[\text{Amplitude}=4\sqrt{2}.\] Hence, the correction option is [d].


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