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JEE Main & Advanced Sample Paper JEE Main Sample Paper-18

  • question_answer
    A body of mass m is released from a height h to a scale pan hung from a spring as shown in figure. The spring constant of the spring is k, the mass of the scale pan is negligible and the body does not bounce relative to the pan, then the amplitude of vibration is

    A)  \[\frac{mg}{k}\sqrt{\left( 1+\frac{2\,hk}{mg} \right)}\]

    B)  \[\frac{mg}{k}\]

    C)  \[\frac{mg}{k}\left[ 1+\sqrt{\left( 1+\frac{2\,hk}{mg} \right)} \right]\]

    D)  \[\frac{mg}{k}-\frac{mg}{k}\left[ \sqrt{\left( 1-\frac{2hk}{mg} \right)} \right]\]

    Correct Answer: A

    Solution :

     \[mg(h+y)=1\text{/}2\,x{{y}^{2}}\] \[y=\frac{mg}{k}+\frac{mg}{k}\left[ \sqrt{1+\frac{2hk}{mg}} \right]\] So, amplitude of vibration \[a=y-mg\text{/}k\]    \[=\frac{mg}{k}\left[ \sqrt{1+\frac{2hk}{mg}} \right]\]


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