Question

If the earth suddenly contracts to half its present radius, what would be the length of the day? Show your working.

Answer 1

By Kepler's law ,we know that the angular momentum of the earth is conserved about its own axis.

so, $m{\omega }^{2}R=m{\omega }^2(\frac{R}{2}$)

$\frac{1}{T^2}R=\frac{1}{T^{\prime 2}}\times \frac{R}{2}$

$T^{\prime 2}=\frac{T^2}{2}$

$T^{\prime }=\frac{T}{\sqrt{2}}$

$T^{\prime }=\frac{24}{\sqrt{2}}=19.97hours$

Length of the day would be 19.97 hours.