Answer to Question #158119 in Physics for Lee

Question

Assume that the temperature effects of glaciations can be

represented by a periodic surface temperature with a period of 104 yr. If

it is desired to drill a hole to a depth that the temperature effect of the

glaciations is 5% of the surface value, how deep must the hole be drilled?

Assume κ = 1 mm2 s−1.

Answer 1

$$d=\sqrt{\frac{2k}{\omega}}\\d=\sqrt{\frac{kT}{\pi}}\\d=\sqrt{\frac{(10^{-6})(10^4)}{\pi}}=0.056\ m=56\ mm$$