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
−38G
C
−34G
D
−4G
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Updated on : 2022-09-05
Solution
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Correct option is D)
Gravitational potential at distance x, V=−xGm
⇒ Gravitational Potential at origin, V=−12G−22G−42G−82G−−−−to∞
⇒V=−2G{11+21+41+81++++to∞}
⇒{11+21+41+81++++to∞} is GP series Where a=1 and r=21