Infinite number of bodies, each of mass 2 kg are situated on X-axis at distance 1m, 2 m, 4 m, 8 m respectively from the origin. The resulting gravitational potential due to this system at the origin will be [NEET 2013]

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-G

- (8/3)

-(4/3))G

-4G

answer is D.

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Detailed Solution

The resulting gravitational potential, V=-2G11+12+14+18+…⇒ V=-2G1+12+122+123⋯Using Binomial expansion, V=-2G1+12-1⇒ V=-2G1-12=-2G12=-4G

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