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JEE Main & Advanced JEE Main Paper (Held On 19 April 2014)

  • question_answer
    The gravitational field in a region is given by \[\overset{\to }{\mathop{g}}\,=5N/kg\hat{i}+12N/kg\hat{j}.\]The change in the gravitational potential energy of a particle of mass 1 kg when it is taken from the origin to a point (7 m, ? 3 m) is:     JEE Main Online Paper (Held On 19 April 2016)

    A) 71 J                                        

    B) 13 58 J

    C) 71 J                                        

    D) 1 J

    Correct Answer: D

    Solution :

     Gravitational field, \[I=\left( 5\hat{i}+12\hat{j} \right)N/kg\] \[I=-\frac{dv}{dr}\] \[v=-\left[ \int\limits_{0}^{x}{{{I}_{x}}dx}+\int\limits_{0}^{y}{{{I}_{y}}dy} \right]\] \[=-\left[ {{I}_{x}}.x+{{I}_{y}}.y \right]\] \[=-\left[ 5\left( 7-0 \right)+12\left( -3-0 \right) \right]\] \[=-\left[ 35+\left( -36 \right) \right]=1J/kg\] i.e., change in gravitational potential 1 J/kg. Hence change in gravitational potential energy 1 J


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