Question

Infinite number of bodies, each of mass 2kg are situated on X-axis at distance `1m,2m,4m,8m,` respectively from the origin, What is the resulting gravitational potential due to this system at the origin ?

Answer 1

The resulting gravitational potential
`V=-2G((1)/(1)+(1)/(2)+(1)/(4)+(1)/(8)....)=-2G(1+(1)/(2)+(1)/(2^(2))+(1)/(2^(3)).....)`
`rArr V=(-2G)/((1-(1)/(2)))=(-2G)/((1)/(2))=-4G`.