Infinite number of bodies, each of mass `2kg`, are situated on `x`-axis at distance `1m,2m,4m,8m.........` respectively, from the origin. The resulting gravitational potential the to this system at the origing will be

Options

A. `-4/3 G`
B. `-4G`
C. `-G`
D. `-8/3 G`

Answer

B

Explanation

The resulting gravitational potential at the origin O due to each of mass 2 kg located at positions as shown in figure is

` V = - (G xx 2)/(1) - (G xx 2)/(2) - (G xx 2)/(4) - G xx 2)/(8)`
`= - 2G [1 + 1/2 + 1/4 + 1/8 + .....] = - 2G [(1)/(1 - 1/2)] = -2G [2/1] = -4G`