An infinite number of particles each of mass `m` are placed on the positive X-axis of `1m, 2m, 4m, 8m,...` from the origin. Find the magnitude of the resultant gravitational force on mass `m` kept at the origin.

Explanation

The resultant gravitatiional force
`F=(Gm^(2))/1+(Gm^(2))/4+(Gm^(2))/16+……………`
`=Gm^(2)(1+1/4+1/16+………..)`
`=Gm^(2)(1/(1-1/4))=4/3Gm^(2) ( :. S_(oo)=a/(1-r))`