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Gravitational potential for a point mass is given by - $- \sum_{i = 1}^{n} \frac{{GM}_{i}}{x_{i}}$
where x is the distance of the mass from a point and M is the mass of the body. Find the total potential at the origin for each one kg mass placed at 1m, 2m, 4m, and 8m... up to infinity.

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-4G

-2G

-1.5G

(-2/3)G

answer is B.

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Detailed Solution

According to the formula

potential for the system of mass = $V = - G (\frac{1}{1} + \frac{1}{2} + \frac{1}{4} + \frac{1}{8} + . . . . . . .)$

$applying G . P series formula S = \frac{1}{1 - r} if r is less than 1 and no of turns infinity$

$V = - G \frac{1}{1 - \frac{1}{2}} = - 2 G$

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