CMC Medical CMC-Medical VELLORE Solved Paper-2010

  • question_answer
    The maximum velocity of a particle executing SHM is v. If the amplitude is doubled and the time period of oscillation decreased to \[\frac{1}{3}\] of its original value, the maximum velocity becomes

    A)  18 v                                      

    B)  12 v

    C)  6 v                                        

    D)  3 v

    E)  None of these

    Correct Answer: C

    Solution :

                    Maximum velocity \[{{v}_{\max }}=A\omega \] \[\omega =\frac{2\pi }{T}\] \[\therefore \]  \[{{v}_{\max }}=\frac{2\pi A}{T}\]                 \[v\propto \frac{A}{T}\] \[\therefore \]  \[\frac{{{v}_{1}}}{{{v}_{2}}}=\frac{{{A}_{1}}}{{{A}_{2}}}\times \frac{{{T}_{2}}}{{{T}_{1}}}\] \[=\frac{1}{2}\times \frac{1}{3}=\frac{1}{6}\] \[{{v}_{2}}=6{{v}_{1}}\] \[=6\,v\]


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