JEE Main & Advanced Physics Work, Energy, Power & Collision / कार्य, ऊर्जा और शक्ति Sample Paper Topic Test - Work Energy Power

  • 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 :

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

You need to login to perform this action.
You will be redirected in 3 sec spinner