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JEE Main & Advanced Sample Paper JEE Main - Mock Test - 30

  • question_answer
    In figure (a), (b) a stationary spacecraft of mass M is passed by asteroid A of mass m, asteroid B of the same mass w, and asteroid C of mass 1m. The asteroids move along the indicated straight paths at the same speed; the perpendicular distances between the spacecraft on the paths are given as multiples of R. Figure  gives the gravitational potential energy U(f) of the spacecraft- asteroid system during the passage of each asteroid treating time \[t=0\] as the moment when separation is minimum. Which asteroid corresponds to which plot of U(t)'?

    A) \[A-1,\,B-2,\,C-3\]

    B)        \[B-1,\,A-3,\,C-2\]

    C) \[B-1,\,A-2,\,C-3\]          

    D) None of these

    Correct Answer: C

    Solution :

    [c] Potential energy of two particles system is given by,  \[U=-\frac{G{{M}_{1}}{{M}_{2}}}{r}.\] The potential energy of spacecraft and asteroid A When they are at minimum separation, \[{{U}_{A}}=-\frac{GMm}{R}\] The potential energy of spacecraft and asteroid B When they are at minimum separation, \[{{U}_{B}}=-\frac{GMm}{2R}\] The potential energy of spacecraft and asteroid C When they are at minimum separation, \[{{U}_{C}}=-\frac{GM2m}{R}\] The potential energy will be Minimum for (3), Energy will be Maximum for (2).


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