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Q.

Infinite number of  point size masses, each 1kg are placed along the x-axis at x=±1m,±2m,±4m,±8m,±16m.......... The gravitational potential in terms of gravitational constant G at the origin (x=0) is (take gravitational potential at infinity zero.)

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a

-G/2

b

-2G

c

-G

d

-4G

answer is D.

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Detailed Solution

Gravitational potential,
V=2GM(1r1+1r2+1r3+.....)     =2G.1(11+12+14+18+116+...)      =2G(111/2)          (sum  ofinfinite  GP=a1  r)      =4G

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