Question

Suppose that the circumference of Earth is a perfect circle of exactly 25,000 mi. Somebody prepares a wire that is supposed to go around the equator completely but makes it 2 m too long by mistake. If this 2-m-too-long wire were placed around the equator in a perfect circle with the ends of the wire just touching each other, by how much would the wire be off the ground?

Answer 1

The wire will be 31.83 cm off the ground. This result is independent of the circumference of the Earth!!!

Step-by-step explanation:

The circumference c of a circle with radius r can be obtained with the formula:

`c = 2 \pi r`

If the circumference of the earth is
`c_e`, and the radius of the earth is
`r_e`, we get:

`c_e = 2 \ \pi \ r_e`

Now, for a circumference 2 meters to long, we get:

`c_e + 2  \ m  = 2 \ \pi \ r'`

we can obtain how much would the wire be off the ground simply by taking the difference of this equations:

`c_e + 2  \ m -  c_e = 2 \ \pi \ r' - 2 \ \pi \ r_e`

`2  \ m = 2 \ \pi \  (r' - r_e)`

`(r' - r_e) = ( 2  \ m )/( 2 \ \pi)`

`(r' - r_e) = ( 1  \ m )/(  \pi)`

`(r' - r_e) = 31.83 cm`

So, the wire will be 31.83 cm off the ground. This result is independent of the circumference of the Earth!!!