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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a
-G
b
- (8/3)
c
-(4/3))G
d
-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
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]