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

An infinite number of particles each of mass m are placed on the posit

1.	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
Answer» SOLUTION : 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`