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Question

Infinite number of bodies, each of mass 2 kg, are situated on xaxis 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
  1. G
  2. 83G
  3. 43G
  4. 4G

A
G
B
43G
C
4G
D
83G
Solution
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Gravitational potential at distance x, V=Gmx
Gravitational Potential at origin, V=2G12G22G42G8to
V=2G{11+12+14+18++++to}
{11+12+14+18++++to} is GP series Where a=1 and r=12
Sum of GP series, S=a1r
V=2G×1112=4G

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