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J & K CET Medical J & K - CET Medical 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 pan, 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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