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.

Explanation

`vec(I_("net"))=vec(I)+vec(I_(2))+vec(I_(3))+vec(I_(4))+…oo` terms
`=("GM")/((1)^(2))hati+("GM")/((2)^(2))hati+("GM"hati)/((4)^(2))+…oo` thems
`="GM"hati(1+(1)/(4)+(1)/(16)+….oo)`
[Here in the GP a = 1 and `r=(1)/(4)`]
So, `vec(I_("net"))="GM"hati[(1)/(1-(1)/(4))]="GM"hati[(1)/((3)/(4))]impliesvec(I_("net"))=(4)/(3)"GM"hati`.