A straight, smooth tunnel is dug through auniform spherical planet of mass density ?P. The tunnel passes through the centerof the planet and is perpendicular to theplanet''s axis of rotation, which is fixed inspace. The planet rotates with a constantangular speed w so that objects in the tunnelhave no apparent weight. Find therequired angular speed of the planet ?.

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)

Approved