An infinite number of particles with mass m are placed on the x axis with distan

Question

An infinite number of particles with mass m are placed on the x axis with distance

a between them, as pictured. Find the total force acting on the particle at the

origin due to all of the other particles.

An infinite number of particles with mass m are placed on the x axis with distance a between them, as pictured. Find the total force acting on the particle at the origin due to all of the other particles. Hint: you will need to set up an infinite sum, which you will need to evaluate using the following: 1/n2 = pi 2/6.

Explanation / Answer

Total force = Gm/a^2 +Gm/(2a)^2 +Gm/(3a)^2 + Gm/(4a)^2.....

==> F= Gm/(a^2*sigma(n^2))

as it is given that

sigma(1/n^2) = pi^2/6

==> F= Gm*pi^2/6a^2

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