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 accelerates uniformly from rest to a speed \[\left( \lambda  \right)\]in time \[\infty \]. The work done on the body till any time t is

    A) \[\frac{1}{2}mv_{0}^{2}\left( \frac{{{t}^{2}}}{t_{0}^{2}} \right)\]

    B) \[\frac{1}{2}mv_{0}^{2}\left( \frac{{{t}_{0}}}{t} \right)\]

    C) \[mv_{0}^{2}\left( \frac{t}{{{t}_{0}}} \right)\]

    D) \[mv_{0}^{2}{{\left( \frac{t}{{{t}_{0}}} \right)}^{3}}\]

    Correct Answer: A

    Solution :

    [a] \[{{v}_{0}}=a{{t}_{0}}\]        \[\therefore \]    \[a=\frac{{{v}_{0}}}{{{t}_{{}}}}\]
    Velocity at any time t would be
      \[V=at=\left( \frac{{{v}_{0}}}{{{t}_{0}}} \right)t\]
       \[\therefore \]  Kinetic energy,
              \[\text{K=}\frac{1}{2}m{{v}^{2}}=\frac{1}{2}m{{\left( \frac{{{v}_{0}}}{{{t}_{0}}} \right)}^{2}}{{t}^{2}}\]
       From work energy theorem
      or   \[W=\frac{1}{2}mv_{0}^{2}\left( \frac{{{t}^{2}}}{t_{0}^{2}} \right)\]

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