Infinite number of spheres , each of mass m are placed on the X- axis at distance 1,2,4,8,16, … meter from origin . The magnitide of the gravitational field at the origin is

Options

A. `(2)/(3)Gm`
B. `(4)/(3)Gm`
C. Gm
D. 6 Gm

Explanation

Gravitaiona field at the origin due to mass at 1,2,4,8,16 …..

`=(Gm)/((1)^(2))+(Gm)/((2)^(2))+(Gm)/((4)^(2))+(Gm)/((8^(2)))....`
`=Gm[1+(1)/(4)+(1)/(16)+......]=(4Gm)/(3)`