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when you are in a rotating reference frame then you experience the radially outward centrifugal force.
in this case the centrifugal force balances the gravitational force of attraction.
that is G*(4/3)*πr3Pm/r2 = mrw2.
here m = mass of the particle, r = distance of the particle from the center of the planet along the tunnel that is the radial distance of the particle.
this gives w = {(4/3)*πGP}(1/2)
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