Question

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

• A. $- 4 G$
• B. $- G$
• C. $- \frac{8}{3} G$
• D. $- \frac{4}{3} G$

Answer 1

Answer: (A)

$- 4 G$

Answer 2

$V = - G (2)\bigg[\frac{1}{1} +\frac{1}{2}+ \frac{1}{4} + \frac{1}{8}+...........\bigg]$
$= - 2G\bigg[ \frac{1}{1 - 1/2}\bigg] = - 4G$