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Infinite number of bodies, each of mass 2 kg are situated on x-axis at distance 1 m, 2 m, 4 m, 8 m, ...., respectively, from the origin. The resulting gravitational potential due to this system at the origin will be:
A
−4G
B
−G
C
$-\frac{8}{3}G$
D
$-\frac{4}{3}G$
Detailed Solution
$V = -G(2)\left[\frac{1}{1} + \frac{1}{2} + \frac{1}{4} + \frac{1}{8} + \dots\right]$
$= -2G\left[\frac{1}{1 - 1/2}\right] = -4G$
$= -2G\left[\frac{1}{1 - 1/2}\right] = -4G$