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//3)G`
C. `-(4//3)G`
D. `-4G`

Answer

D

Explanation

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