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?

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fenixbm fenixbm · Answer 1 · 2019-10-10T21:51:48+02:00

Answer:

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

Explanation:

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

[tex]c = 2 \pi r[/tex]

If the circumference of the earth is [tex]c_e[/tex], and the radius of the earth is [tex]r_e[/tex], we get:

[tex]c_e = 2 \ \pi \ r_e[/tex]

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

[tex]c_e + 2 \ m = 2 \ \pi \ r'[/tex]

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

[tex]c_e + 2 \ m - c_e = 2 \ \pi \ r' - 2 \ \pi \ r_e[/tex]

[tex] 2 \ m = 2 \ \pi \ (r' - r_e) [/tex]

[tex] (r' - r_e) = \frac{ 2 \ m }{ 2 \ \pi} [/tex]

[tex] (r' - r_e) = \frac{ 1 \ m }{ \pi} [/tex]

[tex] (r' - r_e) = 31.83 cm [/tex]

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