Infinite number of bodies, each of mass 2kg, are situated on x−axis at distance 1m,2m,4m,8m,....... respectively, from the origin. The resulting gravitational potential due to this system at the origin will be
A
−G
B
−83G
C
−43G
D
−4G
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Solution
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Gravitational potential at distance x, V=−Gmx
⇒ Gravitational Potential at origin, V=−2G1−2G2−2G4−2G8−−−−to∞
⇒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=a1−r
⇒V=−2G×11−12=−4G
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