Question

Lets say we can drill a tunnel straight through north- and southpole. Describe the movement of a rock that falls from northpole. Lets say the earth has a homogenous density and discard friction. Calculate after how much time the stone reaches the mid-point of the earth.

Answer 1

Some already answer this question, but forgot to actually explain it...

Answer 2

are you familiar with the shell theorems..?

Answer 3

kind of, yes. i have some formulas etc...

Answer 4

for a homogenous ... = K=GmMr/R^3

Answer 5

right?

Answer 6

homogenous shell i mean

Answer 7

yes..its actually a part..but you are correct..they are..
1)A spherically symmetric body affects external objects gravitationally as though all of its mass were concentrated at a point at its centre.
2)If the body is a spherically symmetric shell (i.e., a hollow ball), no net gravitational force is exerted by the shell on any object inside, regardless of the object's location within the shell.

Answer 8

By using these two laws..and supposing the EARTH's core is not so hot...:D
we can describe the motion of rock..

Answer 9

alright, so the radius of earth is: 6371 km and mass= 5,9737 x10^24 kg

Answer 10

and the second law doesn't apply to the question? because it's not hollow..right?

Answer 11

@RaGhavv

Answer 12

actually,,the second law could still be applied,,if needed,,i mean,,we can assume earth to be made up of ""infinite number of hollow shells"",,which is how the shell theorem is proved..
the only context of its application would be changed..here the ""accn due to gravity"" will play a good role..analyse wat will happen to it as the rock goes down...

Answer 13

i mean try visualising the earth to be made up of infinite no. of shell,,and then think(using the shell theorems)...

Answer 14

so no gravitational force is exerted on the rock

Answer 15

explain me why,being consistent with the the 2 laws??

Answer 16

The rock will execute simple harmonic motion according to the formula 2pi under the root R/g.