Question

# Infinite number of bodies, each of mass 2 kg, are situated on x−axis 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

A
G
B
83G
C
43G
D
4G
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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