Infinite number of masses , each 1 kg ,are placed along the x-axis at `x=+-1m,+-2m,+-4m,+-8m,+-16m`..... The mangnitude of the resultant gravitational potentrial in terms of gravitational constant G at the origin (x=0) is

Options

A. G/2
B. G
C. 2G
D. 4G

Answer

C

Explanation

Gravitational potential
`V=GM((1)/(r_(1))+(1)/(r_(2))+(1)/(r_(3))+...)`
`=Gxx1((1)/(1)+(1)/(2)+(1)/(4)+(1)/(8)+(1)/(16)+....)`
`=G((1)/(1-1//2)) " " (because"sum of GP"=(a)/(1-r))`
=2G