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A very large number of particles of sam...

A very large number of particles of same mass m are kept at horizontal distance of 1m, 2m, 4m, 8...... (upto infinity) from origin. The total gravitational potential at origin is

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The resultant gravitational force
`F = (Gm^(2))/(1) + (Gm^(2))/(4) + (Gm^(2))/(16)+…..`
`= Gm^(2)((1)/(1)+(1)/(4)+(1)/(16)+….) = Gm^(2)((1)/(1-(1)/(4)))`
(`because` sum of the infinit trms in G.P is `S_(prop) = (a)/(1-r)`)
`= (4)/(3)Gm^(2)`
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