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A very large number of particles of same mass m kept at horizontal distance of 1m, 2m, 4m and 8m and so on from (0,0) point the total gravitational potential at point (0,0) is

A very large number of particles of same mass m kept at horizontal distance of 1m, 2m, 4m and 8m and so on from (0,0) point the total gravitational potential at point (0,0) is

Grade:11

1 Answers

Arun
25750 Points
6 years ago
Dear Aditya
 
Gravitational potential at point r is given by,
V = - G*m/r
 
According to the problem the gravitational potential by infinite masses at the origin is,
 
V = -G*m (1 + 1/2 + 1/4 + 1/8+...)
 

This is a geometric series with ratio 1/2

So, 

V = -G*m*2.         As(sum of infinite terms of G.P. = 1/(1-1/2 ) = 2

= - 2*G*m

 

Regards

Arun(askIITians forum expert)

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