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

  • question_answer
    A block of mass m moving with a velocity \[{{v}_{0}}\]on a smooth horizontal floor collides with a light spring of stiffhess k that is rigidly fixed horizontally with a vertical wall. If the maximum force imparted by the spring on the block is F, then

    A) \[F\propto \sqrt{m}\]

    B) \[F\propto \sqrt{k}\]

    C) \[F\propto {{v}_{0}}\]

    D) None of these

    Correct Answer: D

    Solution :

    [d] Energy conservation between the positions A and B requires that
    \[\Lambda PE+KE=0\]
    or         \[\frac{1}{2}k{{x}^{2}}-\frac{1}{2}mv_{0}^{2}=0\]
      \[\therefore \] \[x=\sqrt{\frac{m}{k}}{{v}_{0}}\]
      \[\therefore \,\,\,\,\,\,{{F}_{\max }}=kx=\sqrt{mk}{{v}_{0}}\]
      or        \[{{F}_{\max }}\propto \sqrt{k}\propto \sqrt{m}\propto {{v}_{0}}\]

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