Infinite particles each of mass 'M' are placed at positions `x=1 m, x=2m, x=4 m .... prop`. Find the gravitational field intensity at the origin.
ltimg src="https://d10lpgp6xz60nq.cloudfront.net/physics_images/ALN_PHY_2_C05_S01_009_Q01.png" width="80%"gt

Explanation

`vec(I)_("net")=vec(I)_(1)+vec(I)_(2)+vec(I)_(3)+vec(I)_(4)+...oo` terms
`=(GM)/((1)^(2)) hat(i)+(GM)/((2)^(2)) hat(i)+(GM hat(i))/((4)^(2))+....oo` terms `=GM hat(i) (1+1/4+1/16+...oo)" "["Here in the GP a = 1 and "r=1/4]`
So, `vec(I)_("net")=GM hat(i) [1/(1-1/4)]=GM hat(i) [1/((3/4))] implies vec(I)_("net")=4/3 GM hat(i)`