Infinite no.of bodies, each of mass 3kg are situated at distances 1m, 2m, 4m, 8m....... respectively on x-axis. The resultant intensity of gravitational field at the origin will be

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Solution

The correct option is D
4G

Intensity at the origin = $\frac{G M}{r_{1}^{2}} + \frac{G M}{r_{2}^{2}} + \frac{G M}{r_{3}^{2}} + \frac{G M}{r_{4}^{2}} + . . . . . .$

= $G M [1 + \frac{1}{4} + \frac{1}{16} + \frac{1}{16} + \frac{1}{64} + . . . . . .] = G M (\frac{1}{1 - \frac{1}{4}}) == G M \times \frac{4}{3} = G \times 3 \times \frac{4}{3} = 4 G$ [As M=3kg given]

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Infinite no.of bodies, each of mass 3kg are situated at distances 1m, 2m, 4m, 8m....... respectively on x-axis. The resultant intensity of gravitational field at the origin will be

The correct option is D 4G Intensity at the origin =GMr21+GMr22+GMr23+GMr24+...... =GM[1+14+116+116+164+......]=GM(11−14)==GM×43=G×3×43=4G [As M=3kg given]