What would happen to you frll along a straight tunnel through the center of Earth. The problem has been analyzed ever since Galileo considered it. However, the most enchanting version is the one about Alice where she falls down the rabbit hole in ''Alice in Wonderland'', which Lewis CArroll wrote to entrain the (real) Alice Liddell when she was a child. Here is a passage from Alice :
Either the well was very deep, or she fell very slowly, for she had plenty of time as he went down to look about her, and to wonder what was going to happen next. First, she tried to look down and make out what she was coming to, but it was too dark to see anything : then she looked at the sides of the well, and noticed that they were filled to see anything : then she looked at the sides of the well, and noticed that they were filled with cupborad and look - shelves , here and there she saw maps and pictures hung upon pegs. She took down a jar from one of the shelves as the passed : it was labeled ''ORANGE MARMALADE'', but to her great disappointment it was empty : she did not like to drop the jar, for fear of killing somebody underneath, so managed to put it into one of the cupboards as she fell past it ..... Down, down, down. Would the fall never come to end ? ''I wounder how many miles I' ve fallen by this time ?'' she said aloud. ''I must be getting somehere near the centre of the earth.'' If Alice did fall down a tunel to the center of the Earth, would she drift slowly enough to see or grab things along the way ? Would the gravitational force that pulled her downward wane during the descent ? These questions were hot topice in Carroll's time, but Gallileo had the correct explanation long before then.
What is the velocity of Alice at R/2 from centre of the earth.