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J & K CET Engineering J and K - CET Engineering Solved Paper-2006

  • question_answer
    Time period of a spring mass system is T. If this spring is cut into two parts whose lengths are in the ratio \[1:3\] and the same mass is attached to the longer part, the new time period will be

    A)  \[\sqrt{\frac{3}{2}}T\]

    B)  \[\frac{T}{\sqrt{3}}\]

    C)  \[\frac{\sqrt{3}T}{2}\]

    D)  \[\sqrt{3}T\]

    Correct Answer: B

    Solution :

    The spring mass system oscillates in SHM, its time period is given by \[T=2\pi \,\sqrt{\frac{m}{k}}\] When spring is cut in ratio \[1:3\] the new time constant is \[k'=3k\] \[\therefore \] \[\frac{T}{T'}=\sqrt{\frac{3k}{k}}\] \[\Rightarrow \] \[T'=\frac{T}{\sqrt{3}}\]


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