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A straight, smooth tunnel is dug through a uniform spherical planet of mass density ? P. The tunnel passes through the center of the planet and is perpendicular to the planet''s axis of rotation, which is fixed in space. The planet rotates with a constant angular speed w so that objects in the tunnel have no apparent weight. Find the required angular speed of the planet ?.

A straight, smooth tunnel is dug through a
uniform spherical planet of mass density ?
P. The tunnel passes through the center
of the planet and is perpendicular to the
planet''s axis of rotation, which is fixed in
space. The planet rotates with a constant
angular speed w so that objects in the tunnel
have no apparent weight. Find the
required angular speed of the planet ?.

Grade:12

1 Answers

SOURAV MISHRA
37 Points
8 years ago

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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