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

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

TestHub · Accepted Answer

Gravitational potential at a distance r from a mass = $V = \frac{G M}{r}$

Net Gravitational potential = $\sum \frac{G M}{r_{i}}$

$V = G M (\frac{1}{r_{1}} + \frac{1}{r_{2}} + \frac{1}{r_{3}} + \dots)$

$= G \times 1 (\frac{1}{1} + \frac{1}{2} + \frac{1}{4} + \frac{1}{8} + \frac{1}{16} + \dots .)$

$(∴ s u m o f G P = \frac{a}{1 - r})$

$V=2 G$

Physics - Gravitation Question with Solution | TestHub

Options:

Doubts & Discussion