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

Options

A. `-G`
B. `-8/3G`
C. `-4/3G`
D. `-4G`

Answer

D

Explanation

`V=-2G[1/1+1/2+1/4+1/8........]`
`=-2G[1+1/2+1/(2^(2))+1/(2^(3)).......]`
`=-2G1/((1-1/2))=-4G`