Infinite particles each of mass m are placed at positions x=0,1,2,4,8........∞ metersrespectively . The magnitude of gravitational force on particle at orgin x=0 is

F=F1+F2+F3+……∞F=Gmm112+122+142+…… F=Gm211−14F=4Gm23

Infinite particles each of mass m are placed at positions x=0,1,2,4,8........∞ metersrespectively . The magnitude of gravitational force on particle at orgin x=0 is

F=F1+F2+F3+……∞F=Gmm112+122+142+…… F=Gm211−14F=4Gm23

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Infinite particles each of mass m are placed at positions $x = 0, 1, 2, 4, 8 ........ \infty meters$ respectively . The magnitude of gravitational force on particle at orgin $(x = 0)$ is

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$\frac{4 {Gm}^{2}}{3}$

$\frac{3 {Gm}^{2}}{4}$

$\frac{{Gm}^{2}}{2}$

$\frac{4 {Gm}^{2}}{9}$

answer is A.

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Detailed Solution

$\begin{array}{l} F = F_{1} + F_{2} + F_{3} + \dots \dots \infty \\ F = Gmm [\frac{1}{1^{2}} + \frac{1}{2^{2}} + \frac{1}{4^{2}} + \dots \dots] \end{array} \begin{array}{l} F = {Gm}^{2} [\frac{1}{1 - \frac{1}{4}}] \\ F = \frac{4 {Gm}^{2}}{3} \end{array}$