An infinite number of particles each of mass m are placed on the positive x-axis at 1m, 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-axis at 1m, 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)))` (`because` sum of the INFINIT TRMS in G.P is `S_(prop) = (a)/(1-r)`) `= (4)/(3)Gm^(2)`