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Chhattisgarh PMT Chhattisgarh PMT Solved Paper-2006

  • question_answer
    Period of oscillation of mass attached to a  spring and performing SHM is T. The spring is now cut into four equal pieces and the same mass attached to one piece. Now, the period of its simple harmonic oscillations is

    A)  2T                                         

    B)  T/4

    C)  T/2                                       

    D)  T

    Correct Answer: C

    Solution :

    Time period of the mass attached to a spring, \[T=2\pi \sqrt{\frac{m}{k}}\]       ?..(i) When spring is cut into four equal pieces, then new spring constant \[\therefore \]  \[k'=4k\]                              \[\left( \because \,\,k\propto \frac{1}{l} \right)\] \[\therefore \] Time period \[(T)=2\pi \sqrt{\frac{m}{k'}}=2\pi \sqrt{\frac{m}{4k}}\]                                 \[=\frac{1}{2}\times 2\pi \sqrt{\frac{m}{k}}=\frac{T}{2}\]


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