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. 6Gm

Answer

B

Explanation

F= `G(1xxm)/1^2 +G(1xxm)/2^2 +…`
`Gm[1+1/4+1/16 +......]`
= `Gm[1/(1-1/4)]` `[therefore s_infty =a/(1-r)]`
`therefore F= 4/3 Gm`