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

Sum of `n^(th)` term of G.P. –
`S_n=a/(1-r),rlt1`
Where `ato` first term, `rto` common ratio
`V=2GM[1+1/2+1/4+1/8…..]`
`=2GM[1/(1-1/2)]=4GM=4G`