An infinite number of particles each of mass m are placed on the positive x-aris at lm, 2m, 4m, 8m, ----- from the origin. The magnitude of the resultant gravitational force on mass .m. kept at the origin is

Explanation

The resultant gravitational force
`F = (Gm^2)/1+(Gm^2)/4+(Gm^2)/16 +........`
`=Gm^(2)(1/1+1/4+1/16+ .........)= Gm^(2)(1/(1-(1)/4))`
( `:. ` sum of the infinite terms in G.P is `S_(prop) = a/(1-r))=4/3Gm^2`