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  4. Infinite number of bodies, each of mass 6 kg, are situated at distances, 1 m , 2 m , 4 m , 8 m , ldots respectively, on Y -axis, from the origin. The resultant gravitational field intensity at the origin is

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Q. Infinite number of bodies, each of mass $6 kg$, are situated at distances, $1 m , 2 m , 4 m , 8 m , \ldots$ respectively, on $Y$ -axis, from the origin. The resultant gravitational field intensity at the origin is

Gravitation

Solution:

$ F_{o}=G(6 kg )\left[\frac{1}{1^{2}}+\frac{1}{2^{2}}+\frac{1}{4^{2}}+\frac{1}{8^{2}}+\ldots\right]$
$=(6 G)\left[\frac{1}{1-\left(\frac{1}{2}\right)^{2}}\right]=6 G \times \frac{4}{3}=8 G$