Would you be in apparent weightlessness?
Yes, g for you would be zero.
What, exactly, do you mean by "in the middle of thje planet"? If you mean a hollow tube, just large enough to contain you, and assuming that the planet is spherical and uniform, and that you are exactly at the center of the earth, you would feel no net force. For a tiny "bit" on mass on one side of you, there is an equal tiny bit of mass diametrically opposite and at thesame distance from you that will cancel its force.
If you are in the tube, but not at the center of the earth, what net force you would feel depends on your distance from the center of the earth. All mass at distance from the center of the earth greater than your distance has a "cancelling" mass diametrically opposite and will contribute no new force. The mass still closer to the earth than you are will still pull on you as if it were concentrated at the center of the earth. Gravitational force is proportional to the mass beneath you and inversely proportional to the square of the distance to the center of the earth. Since the mass beneath you is itself proportional to the cube of the distance to the center of the earth, the gravitational force you feel inside the earth is proportional to the distance to the center of the earth.
I thought as much; thanks!
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