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JEE Main & Advanced JEE Main Paper (Held On 16 April 2018)

  • question_answer
    Two particles of the same mass m are moving  in circular orbits because of force, given by \[F(r)=\frac{-16}{r}-{{r}^{3}}\]The first particle is at a distance \[r=1\]and the second, at\[r=4.\]The best estimate for the ratio of kinetic energies of the first and the second particle is closest to [JEE Main 16-4-2018]

    A) \[{{10}^{-1}}\]                                

    B) \[6\times {{10}^{-2}}\]

    C) \[6\times {{10}^{2}}\]                     

    D) \[3\times {{10}^{-3}}\]   

    Correct Answer: B

    Solution :

     The $ force is required for the circular motion of the body Hence\[|F|=\frac{m{{v}^{2}}}{r}\] \[\frac{m{{v}^{2}}}{r}=\frac{16}{r}+{{r}^{3}}\] \[m{{v}^{2}}=16+{{r}^{4}}\] K.E. \[=\frac{m{{v}^{2}}}{2}=8+\frac{{{r}^{4}}}{4}\] Putting the value of\[r=1\]and \[r=4\]taking the ratio We get the\[\approx 6\times {{10}^{-2}}\]


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