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 3910 kg/m3 , and it has a radius ofR=5.83e6m. What is the speed of the message packet as it passes apoint of distance 0.480R from the center of the planet?

How long does it take for a message to pass from one side of theplanet 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 v = (GM/r)^(1/2) G = 6.67 * 10^-11 Nm^2/kg^2,M = * V = *(4/3)R^3 and r = 0.480R = 3910 kg/m^3 and R = 5.83 * 10^6 m

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