Tying the Earth

Assume for a moment that the earth is a perfectly uniform sphere of radius 6400 km. Suppose a thread equal to the length of the circumference of the earth was placed along the equator, and drawn to a tight fit. Now suppose that the length of the thread is increased by 12 cm, and that it is pulled away uniformly in all directions. By how many cm, will the thread be separated from the earth's surface?

Answer:

1.908 cm.

Let the outer circle have radius as 6400+h cm and therefore its circumference is 2*Pi*(6400+h) Earth's circumference is 2*Pi*6400. Hence the difference = 2*Pi*h = 12 cm. Therefore
h=1.908 cm. It is worthwhile to note that this factor does not involve the radius of the sphere and is independent of it. This means that irrespective of the size of the sphere, i.e. irrespective of the radius of it, whether it is a giant globe or a small tennis ball, it holds good.