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 infinite termsin G.P. is `S_prop =a/(1-r)`) `=4/3Gm^2`