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

Question

Infinite number of masses, each 1 kg, are placed along the x -axis at x = ± 1 m , ± 2 m , ± 4 m , ± 8 m , ± 16 m ..... The magnitude of the resultant gravitational potential in terms of gravitational constant G at the origin ( x = 0 ) is, G, 3 G, 2 G, 8 G

MARKS App · Accepted Answer

Gravitational potential at a distance r from a mass = V = G M r Net Gravitational potential = ∑ G M r i V = G M 1 r 1 + 1 r 2 + 1 r 3 + … = G × 1 1 1 + 1 2 + 1 4 + 1 8 + 1 16 + … . ∴ s u m o f G P = a 1 - r V=2 G

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