Suppose there is a rope tied around the equator of the Earth, and the equator is a perfect circle. If I were to add 1 meter to the rope (assuming it spreads out evenly) what would the distance between the Earth and the rope? The radius of the Earth is 6400 km.

Question

parthkohli · Answer

Oh my, my. 

I've had this question asked by my cousin.

parthkohli · Answer

$$l = 2  \pi r = 12800 \pi ~km$$$$\text{New length,  }l_0 = 2\pi r + 1 = 12800 \pi + 1 =  2\pi R_0$$Where $R_0$ is the new radius after adding 1 metre. Now, if you think about it carefully, the distance between the Earth and the rope is actually the difference in radii, right? So you need to find $R_0 - r$

parthkohli · Answer

$$R_0 = \dfrac{12800\pi + 1}{2\pi} = 6400 + \frac{1}{2\pi}$$$$r = 6400$$Therefore, the distance between the rope and the Earth$$R_0 - r = \dfrac{1}{2\pi }$$

anonymous · Answer

ParthKholi do you have phd in math

anonymous · Answer

What does the R0 and L0 stand for?

anonymous · Answer

@ParthKohli

parthkohli · Answer

I've written in my answer that $R_0$ is the new radius of the rope after 1 m is added and $l_0$ is the new length.