The residents of a small planet have bored a holestraight through its center as

Question

The residents of a small planet have bored a holestraight through its center as part of a communications system. Thehole has been filled with a tube and the air has been pumped out ofthe tube to virtually eliminate friction. Messages are passed backand forth by dropping packets through the tube. The planet has adensity of 3580 kg/m3, and it has a radius of R=5.75E+6m. What is the speed of the message packet as it passes a point adistance of 0.660R from the center of the planet? How long does it take for a message to pass from one side ofthe planet to the other?

Explanation / Answer

the centripetal force on the message packet is F = (m * v^2/r) or (GMm/r^2) = (m * v^2/r) or (GM/r) = v^2 or v = (GM/r)^(1/2) G = 6.67 * 10^-11 Nm^2/kg^2,M = * V = *(4/3)R3 and r = 0.660R

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