
What happens if a hole is dug through the diameter
of the earth and a stone is dropped on it? 
Question Date: 20150206   Answer 1:
Awesome question! For now, let's assume that the
earth is solid all the way through so you actually
can drill a hole through it (there's really tons
of liquid mantle in the center which would just
fill in any hole once it gets deep enough). For
now, let's also assume that there's no air in the
hole, so that the stone doesn't feel any
resistance as it falls.
So, what happens? Well, you might know
that as you get closer to the center of the earth,
the force of gravity actually decreases  that's
because once you're underground, there's some mass
above you that exerts an upward gravitational pull
on you. At the center of the earth, the net force
of gravity is zero, because the earth's mass is
pulling on you equally in all directions (that
means you'd be weightless at the center of the
earth!).
So when you drop the stone, it'll start
accelerating downwards, but as it goes deeper down
the hole its acceleration gradually decreases
(though its speed keeps growing). Once it
gets to the center of the earth, the stone's
acceleration reverses  it starts to slow down and
accelerate back towards the end of the hole you're
standing on. Once it gets to the other end of the
hole (on the other side of the world), it slows
down to the stop, and starts falling back down the
hole again, back towards you. It repeats the
process, and you'd see the stone come back up to
you from the hole, exactly back to where you
dropped it from!
If you do out the math, it turns out it takes
a little less than 90 minutes for this cycle to
happen. If you don't catch the stone, it'll just
keep falling up and down over and over again,
taking 90 minutes for each trip.
What if there's so air in the hole?
Then the stone would feel some resistance from the
air, which would slow it down. It still
oscillates back and forth, but each time it comes
up from the center of the earth, it gains less
height than it did the previous time. Eventually,
it ends up stopping right at the center of the
Earth, where it stops moving and just floats there
(where it's weightless, remember!).
I hope these help!
  Answer 2:
Of course the earth heats up as we go down and the
core is at a temperature of about 8000 Kelvin
degrees!! So, this is STRICTLY a thought
experiment; but if you could do this, the stone
would start at surface and accelerate
downwards. However its rate of acceleration
would gradually decrease so that when it was at
the center it would have a high velocity that
would be constant. Then as it moved through the
other side, the stone would decelerate until it
had zero velocity at the other side… only to fall
BACK down the hole and accelerate again!! So,
it would be like a pendulum going back and
forth from the north pole to the south pole and
back again forever.
  Answer 3:
Good question! We would have to make some serious
approximations for a reasonable (and perhaps
wanted) answer to formulate. Let’s assume we are
digging through the earth’s axis of rotation,
because otherwise the Coriolis Effect will
occur.
Let’s also ignore the massive engineering project
that would enable this holedigging project,
because digging through thousands of miles of
super highpressure, hightemperature molten core
is no easy business. Finally, let’s just assume a
vacuum inside of that hole. If we take into
account these approximations, then you would
expect a rock dropped down this shaft to reach all
the way through to the other side of Earth, and
keep oscillating back and forth. Here is a good
explanation video by Minute Physics on YouTube.
watch here
  Answer 4:
Assuming no air resistance and the hole staying a
hole (part of the interior of the earth is
molten), the stone would oscillate back and forth
through the center of the earth to either end of
the hole, much the way that a pendulum oscillates
(but with friction).
  Answer 5:
This is a cool question about gravity! Let us
start by assuming Earth has a solid core. In
reality, the earth has a liquid mantle layer
beneath the crust so we wouldn't actually be able
to dig a hole through the center of the
planet. Furthermore, let's assume no air
resistance once we dig this hole to the other side
of the world that we've thought of. Let's also say
we drilled the hole so it basically makes a
"tunnel" from the north pole to the south pole.
If we drop a stone through the tunnel from the
north pole, it will initially accelerate towards
the south pole at a decreasing rate as it moves,
until it reaches the center of the Earth. Once it
reaches the center of the earth, it will
decelerate (have a negative acceleration) at an
increasing rate as it moves, but still be moving
toward the south pole. The reason it will start
decelerating is because gravity is weaker
closer to the center of the earth. As a rough
approximation for why this happens, we can look at
the equation for gravitational acceleration as a
function of radius:
g=G M/r^{2}
where G is the gravitational constant,
andM is the mass contained within the
radius r. If we further assume that earth
has a constant density:
M = (4/3)*pi*density*r^{3}.
Plugging this in for M in the equation for g
would give
g=(4pi/3)G*density*r
As you can see, g is proportional to the radius
from the center of the earth. As we approach
the center of the earth, r gets smaller, and so
does g, the gravitational acceleration. Thus,
when the stone reaches the center of the earth, it
will actually start to decelerate, even though it
is still moving toward the south pole. Once it
reaches the south pole, the stone will start
accelerating at a decreasing rate toward the north
pole. When it reaches the center of the planet
again, it will begin to decelerate again, and
continue this oscillating motion between the north
and south poles!
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