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MGIMS WARDHA MGIMS WARDHA Solved Paper-2011

  • question_answer
    The period of vibration of a mass m suspended from a spring is 2 s. If along with it another mass of 2 kg is also suspended, the period of oscillation increases by Is. The mass m will be

    A)  2 kg                                      

    B)  1 kg

    C)  1.6kg                                   

    D)  2.6kg

    Correct Answer: C

    Solution :

                     Time period\[T=2\pi \sqrt{\frac{m}{k}}\] \[\Rightarrow \] \[T\propto \sqrt{m}\]\[\Rightarrow \] \[\frac{{{T}_{1}}}{{{T}_{2}}}=\sqrt{\frac{{{m}_{1}}}{{{m}_{2}}}}\] Given,\[{{T}_{1}}=2\,s\]and\[{{T}_{2}}=2+1=3s\] \[\therefore \]  \[\frac{2}{3}=\sqrt{\frac{m}{m+2}}\] \[\frac{4}{9}=\frac{m}{m+2}\] \[m=1.6kg\]


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