question_answer

Infinite number of masses, each 1 kg are placed along the x-axis \[\operatorname{at} x=\pm  1 m, \pm  2m, \pm  4m, \pm \]\[8m, \pm 16M\ldots \] the magnitude of the resultant gravitational potential in terms of gravitational constant G at the or g in \[(x=0)\] is

A) G/2

B) G   

C) 2G  

D) 4G

Correct Answer: C

Solution :

[c] \[V=\frac{GM}{r}=-G\left( \frac{1}{1}+\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+....\infty  \right)\] \[=-G\left( \frac{1}{1-1/2} \right)=-2G\]