How does adding 100 cm to a rope around the Earth affect its radius?

[Milind_shyani]

Hi pls read this its worth it.(assujme Earth as a complete sphere)
suppose i stand in india(place where equator passes) right now and now i begin my journey with a rope thousnands of kilometers long i follow the journey exactly on equator and return to the same place in india.means ihave tied a knot on the whole Earth with the rope. the length of the rope would be equal to the lenth of the equator. Now suppose that i increase the lenth of the rope by 100 cm.so now as the rope's lenth haas increased it will get loosened by a small bit.
Now suppose that thousnds of men are standing side by sid along the equator.
now as the rope's lenthg has increased(by 100 cm) the rope would become loose.so these men along the equator will be able to lift the rope.ie the rope has become loose so each men standing side by side along the equator will liftthe rope.now as the rope is lifted by each men equally.the rope would itself form a huge circle whose circumference would be greater then Earth by 100 cm.
now as the circum is greater,the radius(of the circle of rope) would be greater than the radius of the Earth by a very very very small amount. the difference bbetween the radius of the Earth and the radius of the circle of the rope would infact be the measure of the lift by the men of the rope. now this lift would be some 1or2 nanometer as common sense says.lets see the math way
radius of earth=r
radius of the circle of rope=R
now
2piR=2pir+100cm
2piR-2pir=100cm
2pi(R-r)=100cm
R-r=100/2pi
R-r=100/2*3.14
R-r=15.92 cm
Means appr 16 cm.SO BY JUST ADDING 100CM TO THE ROPE THERE IS A DIFF OF 16 CM IN THE RADII. i tried it on a cricket ball,a basket ball and thee answer comes same 16.00 cm
I hope you get the problem if not tell me i will try to explain it in a better way.
courtesy-million to 1

 

[Hootenanny]

Ahh, brings back some memories! This was actually part of the first question at my interview when I applied for my undergad degree at unniveristy.

 

[Milind_shyani]

Hi pls read this its worth it.(assujme Earth as a complete sphere)
suppose i stand in india(place where equator passes) right now and now i begin my journey with a rope thousnands of kilometers long i follow the journey exactly on equator and return to the same place in india.means ihave tied a knot on the whole Earth with the rope. the length of the rope would be equal to the lenth of the equator. Now suppose that i increase the lenth of the rope by 100 cm.so now as the rope's lenth haas increased it will get loosened by a small bit.
Now suppose that thousnds of men are standing side by sid along the equator.
now as the rope's lenthg has increased(by 100 cm) the rope would become loose.so these men along the equator will be able to lift the rope.ie the rope has become loose so each men standing side by side along the equator will liftthe rope.now as the rope is lifted by each men equally.the rope would itself form a huge circle whose circumference would be greater then Earth by 100 cm.
now as the circum is greater,the radius(of the circle of rope) would be greater than the radius of the Earth by a very very very small amount. the difference bbetween the radius of the Earth and the radius of the circle of the rope would infact be the measure of the lift by the men of the rope. now this lift would be some 1or2 nanometer as common sense says.lets see the math way
radius of earth=r
radius of the circle of rope=R
now
2piR=2pir+100cm
2piR-2pir=100cm
2pi(R-r)=100cm
R-r=100/2pi
R-r=100/2*3.14
R-r=15.92 cm
Means appr 16 cm.SO BY JUST ADDING 100CM TO THE ROPE THERE IS A DIFF OF 16 CM IN THE RADII. i tried it on a cricket ball,a basket ball and thee answer comes same 16.00 cm
I hope you get the problem if not tell me i will try to explain it in a better way.
courtesy-million to 1

Now i would like to know that how it happens it is against common sense.

 

[Curious3141]

Why is it against common sense?

 

[Hootenanny]

Now i would like to know that how it happens it is against common sense.

Why is it against common sense? You've just shown why it happens.

Edit: Damn Curious, you're on the ball today...

 

[matt grime]

Hint, what is 1/2pi, approx.

 

[Alkatran]

If you want a common sense reason, consider how a square acts:

Make a big square that fits tightly around a circle (maybe a basketball, maybe the earth). Now increase the circle's radius by 5: how much more square do you need?

Well, you need to add 10cm to each side, while would spread the top and bottom by 10cm and the left and right by 10cm, making it fit tightly around the circle again.

The circle case is very similar to this. Consider that a circle of radius r always has a perimeter less than the perimeter of a square of width 2r: if the circle's perimeter increased any faster than the square's, it would eventually need to have the square inside it!