NEET Sample Paper NEET Sample Test Paper-39

  • question_answer 23) Infinite number of bodies, each of mass 2 kg, are situated on x-axis at distance 1 m, 2 m, 4 m, 8 m, ..... respectively, from the origin. The resulting gravitational potential due to this system at the origin will be

    A) \[-G\]

    B)  \[-\frac{8}{3}G\]

    C) \[-\frac{4}{3}G\]

    D) \[-4G\]  

    Correct Answer: D

    Solution :

     \[V=-2G\left[ \frac{1}{1}+\frac{1}{2}+\frac{1}{4}+\frac{1}{8}- \right]\] \[=-2G\left[ 1+\frac{1}{2}+\frac{1}{{{2}^{2}}}+\frac{1}{{{2}^{3}}}... \right]\] \[=-2G\frac{1}{\left( 1-\frac{1}{2} \right)}=-4G\]

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