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 ?

Options

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

Answer

D

Explanation

`{:(,2kg,2kg,2kg,2kg),(.,.,.,.,.),(x=0,1m,2m,4m,8m...oo):}`
`V_(g)=-(G(2))/(1)-(G(2))/(2)-(G(2))/(4)-(G(2))/(8)...oo`
`V_(g)=-2G[1+(1)/(2)+(1)/(4)+(1)/(8)+...oo]`
`=-2G[(1)/(1-(1)/(2))]=-2G(2)=-4G`