Consider a 40,000 km steel pipe that forms a ring to fit snugly all around the c

Question

Consider a 40,000 km steel pipe that forms a ring to fit snugly all around the circumference of the Earth along its Equator. Suppose people along its length breathe on it so as to raise its temperature by 1 Co. The pipe gets longer. It also is no longer snug. How high does it stand above the ground level now? (To simplify, consider only the expansion of its radial distance from the center of the Earth, and apply the geometric formula that relates circumference C and radius r: C = 2pr. Drawing a picture would help.)

Explanation / Answer

radius of pipe r = 40000/2 pi = 20000/pi , so that
due to thermal expansion increase in radius is
dr = r x coefficiet x temp. rise
= 20000x 12x10^-6 x 1 / 3.14 = 0.076 km

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