Dropping a tennis ball through the earth

[Milind_shyani]

hi
i am confused since many days about this problem which goes as follows
suppose a tube that is longer than the diameter of the Earth is passed inside Earth such that its oother end comes right from the other side of the Earth and the tube passes through the center point of earth.that is suppose i am at the north pole and i pass that tube in the Earth and the tube passes trought the center point of earth.and the other end of the tube is at hte south pole.
now suppose that i drop a tennis ball in the tube at north pole. now will that ball come out from the tube at the south pole.my sir tells that it will come out from the tube at south pole. but i feel the ball will not come out.instead i feel that the ball would become stationary after it comes comes at the center. is my thinking right if right than how can we prove it.
please help me out. i feel it involes torque

 

[Danger]

I would leave torque out of it. The ball will be in a very peculiar decaying orbit. It will pass right through the core, but not to quite as far away as it was dropped from, then fall back toward you. Again, it will stop short of the distance that it fell. Eventually, it will come to rest in the middle. Think of it somewhat like a swinging pendulum. I don't know the math involved.

 

[Doc Al]

Torque is not involved. Start by figuring out the gravitational acceleration of the ball as a function of distance from the center. Hint: If you assume a spherically symmetric earth, the gravitational force within the Earth at any distance r from the center depends only on the mass at points < r (the mass at points > r does not contribute to the gravitational force).

Why do you think the ball would stop at the center?

(Where and whether it stops depends on if you are ignoring friction/air resistance.)

 

[Danger]

Oops! I forgot the reply standard. Sorry, Doc.
Mind you, when I clicked on this thread, it wasn't in the Homework section.

 

[Milind_shyani]

Torque is not involved. Start by figuring out the gravitational acceleration of the ball as a function of distance from the center. Hint: If you assume a spherically symmetric earth, the gravitational force within the Earth at any distance r from the center depends only on the mass at points < r (the mass at points > r does not contribute to the gravitational force).

Why do you think the ball would stop at the center?

(Where and whether it stops depends on if you are ignoring friction/air resistance.)

respectedsir,
i am happy that you have contributed your time to my question.i am obviosly ignoring friction/air resisitance. but instead of torque let's think the other way out that when the ball reaches the center doesn't it stop there due to the gravity which is immense at the center

 

[Doc Al]

i am obviosly ignoring friction/air resisitance.

Nothing is obvious to me, my friend.

but instead of torque let's think the other way out that when the ball reaches the center doesn't it stop there due to the gravity which is immense at the center

Actually, gravity is zero at the center.

 

[Milind_shyani]

Nothing is obvious to me, my friend.

Actually, gravity is zero at the center.

ha ha,
sir your last comment has given me an another question to think about.why is gravity zero at the center

 

[Doc Al]

Because at the center of the earth, all the Earth's mass is "above" you. You are equally surrounded by mass in all directions, thus, by symmetry, the net gravitational force on you must be zero.