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

Options

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

Answer

D

Explanation

Gravitational potential at `O`
`V_(O)=-(Gxx1)/1xx2-(Gxx1)/2xx2-(Gxx1)/4xx2.....oo`
`=-2G[1+1/2+1/4+.....oo]`
`=-2G[1-1//2]=-4G`