Infinite bodies, each of mass $3 K g$ are situated at distances, $1 m, 2 m, 4 m, 8 m, . . . . . . . . .$ respectively on $X$ -axis. The resultant intensity of gravitational field at the origin will be

G

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2 G

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3 G

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4 G

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Solution

The correct option is D $4 G$
Gravitational field at origin: $F = G M (\frac{1}{1^{2}} + \frac{1}{2^{2}} + \frac{1}{4^{2}} + . . . . .) = G \times 3 \times \frac{1}{1 - \frac{1}{4}} = 4 G$

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