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JCECE Engineering JCECE Engineering Solved Paper-2008

  • question_answer
    A mass of \[2.0\,\,kg\] is put on a flat pan attached to a vertical spring fixed on the ground as shown in the figure. The mass of the spring and the pan is negligible. When pressed slightly and released the mass-executes a simple harmonic motion. The spring constant is \[200\,\,N/m\]. What should be the minimum amplitude of the motion, so that the mass gets detached from the pan?     (Take\[g=10m/{{s}^{2}})\]

    A) \[8.0\,\,cm\]

    B) \[10.0\,\,cm\]

    C)  Any value less than\[12.0\,\,cm\]

    D) \[4.0\,\,cm\]

    Correct Answer: B

    Solution :

    Let the minimum amplitude of \[SHM\] is \[a\]. Restoring force on spring                 \[F=ka\] Restoring force is balanced by weight \[mg\] of block. For mass to execute simple harmonic motion of amplitude\[a\]. \[\therefore \]  \[ka=mg\] or            \[a=\frac{mg}{k}\] Here,\[m=2kg,\,\,k=200\,\,N/m,\,\,g=10\,\,m/{{s}^{2}}\] \[\therefore \]  \[a=\frac{2\times 10}{200}=\frac{10}{100}m\]                    \[=\frac{10}{100}\times 1000cm=10\,\,cm\] Hence, minimum amplitude 'of the motion should be \[10\,\,cm\], so that the mass gets detached from the pan.


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