Question

An infinite number of point masses each equal to m are placed at x =1. x = 2, x = 4, x = 8 ……… What is the total gravitational potential at x = 0

• A.
• B. $- 2 G m$
• C. $- 4 G m$
• D.

Answer 1

Answer: (B)

$- 2 G m$

Answer 2

Net potential at origin

$= - G m \left[ \frac { 1 } { 1 } + \frac { 1 } { 2 } + \frac { 1 } { 4 } + \frac { 1 } { 8 } \right]$ $= - G m \left( \frac { 1 } { 1 - \frac { 1 } { 2 } } \right) = - 2 G m$