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

  • question_answer
    The particle is released from a height h. At a certain height, its KE is two times its potential energy Height and speed of the particle at that instant are

    A) \[\frac{h}{3},\,\frac{\sqrt{2gh}}{3}\]

    B) \[\frac{h}{3},\,\frac{\sqrt{gh}}{3}\]

    C) \[\frac{2h}{3},\,\frac{\sqrt{2gh}}{3}\]

    D) \[\frac{h}{3},\,\sqrt{2gh}\]

    Correct Answer: B

    Solution :

    [b] Total mechanical energy = mgh
      As,      \[\frac{KE}{PE}=\frac{2}{1}\]
                \[\frac{KE}{PE}=\frac{2}{1}\] mgh and \[PE=\frac{1}{3}mgh\]
      Height from the ground at this instant,
    \[h'=\frac{h}{3},\] and speed of particle at this instant,
    \[v=\sqrt{2g(h-h')}=\sqrt{2g\left( \frac{2h}{3} \right)}=2\sqrt{\frac{gh}{3}}\]

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