Infinite number of bodies, each of mass 2kg are situated on x-axis at distance 1 m, 2m, 4m, 8m…., respectively, from the origin. The resulting gravitational potential due to this system at the origin will be :
Answer & explanation
Correct answer: option 1
V = - Gm \([\frac{1}{r_1} + \frac{1}{r_2} + \frac{1}{r_3} + ...]\)
V = - Gm \([\frac{1}{2} + \frac{1}{4} + \frac{1}{8} + ...]\)
= - G (2) \([\frac{1}{2} + \frac{1}{4} + \frac{1}{8} + ...]\)
= - G (2) \(\frac{1}{1-\frac{1}{2}}\)
= - 4 G