Particles each of mass M are placed along x-axis at x=1m, x=2m, x=4m, x=8m..... etc., to infinity. Gravitational potential at the origin due to this system of particles is :
2GM
2GM3
4GM3
5GM4
A
5GM4
B
2GM3
C
2GM
D
4GM3
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Solution
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Gravitation potential is given as
EG=GMr
For all the masses, it will be
EG=GM[1r1+1r2+....]
EG=GM[11+12+14+18....]
The right hand side is an infinite geometric series with a common ratio, r=12.
So, the sum is given by
EG=GM[11−12]=GM[11/2]=2GM
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