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JEE Main & Advanced Physics Simple Harmonic Motion Question Bank Spring Pendulum

  • question_answer
    A mass M is suspended from a spring of negligible mass. The spring is pulled a little and then released so that the mass executes simple harmonic oscillations with a time period T. If the mass is increased by m then the time period becomes \[\left( \frac{5}{4}T \right)\]. The ratio of \[T\frac{p}{p-1}\] is      [CPMT 1991]

    A)            9/16                                         

    B)            25/16

    C)            4/5

    D)            5/4

    Correct Answer: A

    Solution :

                       \[T=2\pi \sqrt{\frac{m}{K}}\] Þ \[m\propto {{T}^{2}}\] Þ \[\frac{{{m}_{2}}}{{{m}_{1}}}=\frac{T_{2}^{2}}{T_{1}^{2}}\]            \[\Rightarrow \frac{M+m}{M}={{\left( \frac{\frac{5}{4}T}{T} \right)}^{2}}\Rightarrow \frac{m}{M}=\frac{9}{16}\]


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