Why does adding 1 meter to a rope around the Earth create slack?

[LAF]

First, try to use your own sense.

Take a twine (rope) and put it around a ball, or an orange (sphere).
Now you have the circumference (perimeter) of that sphere.
Take this twine and add 1m more (one more meter - it can be any unit of liner measure).
Put this one meter longer twine around the ball again, keeping it equidistant of the surface (circular orbit, ring).
The twine is aprox. 0,159m of the surface of the ball.

Take a twine (rope) and put it around the Earth equator (sphere).
Now you have the circumference (perimeter) of that sphere.
Take this twine and add 1m more (one more meter - it can be any unit of liner measure).
Put this one meter longer twine around the Earth equator again, keeping it equidistant of the surface (circular orbit, ring).
The twine is aprox. 0,159m of the surface of the earth.

Why does it hapen like this?

 

[Jimmy Snyder]

Why does it hapen like this?

I put the answer is spoiler tags, but this doesn't seem like a brain teaser, more like a homework help. Even so, I give the full answer.

Spoiler

Because the radius is a linear function of the circumference: r = c / 2pi
As a result, if you add 1 meter to the length of the rope (that is, to the circumference) then you will add 1 / 2pi (approx .159 meter) to the radius regardless of the original length.

 

[LAF]

It´s been boring here and I just tried to show something that breaks the common sense.
Now I see I didn´t. I´ll try harder next time...

 

[CEL]

It´s been boring here and I just tried to show something that breaks the common sense.
Now I see I didn´t. I´ll try harder next time...

You have spoiled the problem. The original one is:
Take a rope and tie it tightly around the Earth. Then add 1 meter to the rope. There will be some slack. What kind of animal will pass through the slack?
Intuitively people will say an ant or even a bacterium (I know a bacterium is not an animal, but people say it).
The real answer would be a cat or a bunny.

 

[LAF]

You have spoiled the problem. The original one is:
Take a rope and tie it tightly around the Earth. Then add 1 meter to the rope. There will be some slack. What kind of animal will pass through the slack?
Intuitively people will say an ant or even a bacterium (I know a bacterium is not an animal, but people say it).
The real answer would be a cat or a bunny.

Your way is much better! Thanks.