Speed and time for packet through tunnel in planet's center

[zhenyazh]

Hi,
i am preparing for a test and i really have no idea how to solve the following question.
i would appreciate if some one could give me the direction of solution explaining why things should be done the way the should. i am really clueless here.

The residents of a small planet have bored a hole straight through its center as part of a communications system. The hole has been filled with a tube and the air has been pumped out of the tube to virtually eliminate friction. Messages are passed back and forth by dropping packets through the tube. The planet has a density of 3820 kg/m3, and it has a radius of R=5.31E+6 m.

What is the speed of the message packet as it passes a point a distance of 0.480R from the center of the planet?

How long does it take for a message to pass from one side of the planet to the other?

thanks

 

[tiny-tim]

Hi zhenyazh!

What is the gravitational acceleration at radius r inside the planet?

If it's g(r), then d²r/dt² = -g(r).

 

[zhenyazh]

thanks for your response but i still don't get it.
can u give a more detailed explanantion?