Equator hoop

The equator is approximately 40,000 km long. What would be the gap between an imaginary hoop 40001 km long and the ground? Would a mouse crawl under it?

Final Answer:

x =  159.15 m
y =  1

Step-by-step explanation:

$$\begin{gathered} o_1=40000\text{km} \\ {o}_2=40001\text{km} \\ {r}_1=o_1/(2\pi )=40000/(2\cdot 3.1416)\doteq 6366.1977\text{km} \\ {r}_2=o_2/(2\pi )=40001/(2\cdot 3.1416)\doteq 6366.3569\text{km} \\ \Delta r=r_2-r_1=6366.3569-6366.1977\doteq 0.1592\text{km} \\ x=1000\cdot \Delta r=1000\cdot 0.1592=159.15\text{m} \end{gathered}$$

$$\begin{gathered} x>10cm \\ y=1 \end{gathered}$$

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