Consider a 40,000 km steel pipe in the shape of a ring that fits snuggly all aro

Question

Consider a 40,000 km steel pipe in the shape of a ring that fits snuggly all around the circumference of the Earth. We are heating now the ring so its temperature increased by 1 degree C. Now, the pipe will no longer be snug. How high the ring will now stand above ground level? (Make as many simplifications as necessary). Data: Coefficient of linear expansion for steel is 11*10-6 /degree C. This means, for example, that a 1-meter bar of steel that increases its temperature by 1 degree C will expand 11*10-6 meters (11 micrometers)

Explanation / Answer

Since the pipe is 40000km long, on heating it, its length will increase.

New length of the steel pipe = 40000*(1+alpha*dT)

=40000*(1+11*10^-6*1)

=40000.4 km

so radius of the ring be r.so,

2*pi*r = 40000.4

or r=6366.26 km

so height above the ground = 6366.26 km

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