• # question_answer 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) $-4G$

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