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RAJASTHAN PMT Rajasthan - PMT Solved Paper-2008

  • 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 SHM of time period T. If the mass is increased by m, the time period becomes \[\text{5T/3,}\]then the ratio of\[\frac{m}{M}\]is

    A)  \[\frac{3}{5}\]                                  

    B)  \[\frac{25}{9}\]

    C)  \[\frac{16}{9}\]               

    D)         \[\frac{5}{3}\]

    Correct Answer: C

    Solution :

                    \[T=2\pi \sqrt{\frac{M}{k}}\]                 \[T=2\pi \sqrt{\frac{M+m}{k}}\] \[\Rightarrow \]               \[\frac{5T}{3}=2\pi \sqrt{\frac{M+m}{k}}\] Dividing Eq. (i) by Eq (ii), we have                 \[\frac{3}{5}=\sqrt{\frac{M}{M+m}}\]                 \[\frac{9}{25}=\frac{M}{M+m}\] \[\Rightarrow \]               \[9M+9m=25M\] \[\Rightarrow \]               \[16M=9m\]                 \[\frac{m}{M}=\frac{16}{9}\]


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