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BHU PMT BHU PMT (Screening) Solved Paper-2010

  • question_answer
    A body of mass 6 kg is under a force which causes displacement in it given by\[s=\frac{{{t}^{2}}}{4}m\]where t is time. The work done by the force in 2 sis

    A)  12 J                                       

    B)  9J

    C)  6J                                          

    D)  3J

    Correct Answer: D

    Solution :

                     Distance, \[s=\frac{{{t}^{2}}}{4}\] \[ds=\frac{t}{2}dt\] \[F=ma=\frac{m{{d}^{2}}s}{d{{t}^{2}}}\] \[=\frac{6{{d}^{2}}({{t}^{2}}/4)}{d{{t}^{2}}}=3N\] Now,    \[W=\int_{0}^{2}{F}ds=\int_{0}^{2}{3}\frac{t}{2}dt\]                 \[=\frac{3}{2}\left[ \frac{{{t}^{2}}}{2} \right]_{0}^{2}=\frac{3}{4}[{{(2)}^{2}}-{{(0)}^{2}}]\]                 \[=3J\]


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