JEE Main & Advanced Sample Paper JEE Main Sample Paper-47

  • question_answer
    A force given by the relation \[F=8t\] acts on a body of mass 2 kg initially at rest. Find the work done by this force on the body during first 2 s of its motion.

    A)  64 J                           

    B)  zero             

    C)  - 64 J                         

    D)  None of these

    Correct Answer: A

    Solution :

     Given, \[F=8t\] \[\Rightarrow \]            \[m\frac{dv}{dt}=8t\] or         \[m\int_{0}^{v}{dv=8}\,\int_{0}^{t}{t\,dt}\] \[\Rightarrow \]            \[mv=4{{t}^{2}}\] or         \[m\frac{dx}{dt}=4{{t}^{2}}\] \[\Rightarrow \]            \[dx=\frac{4{{t}^{2}}}{m}dt=2{{t}^{2}}dt\] Now, \[W=\int{F\,dx=\int_{0}^{2}{(8t\times 2{{t}^{2}})}\,dt=64\,\,J}\]

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