Question

5. When the Tohoku earthquake struck Japan in 2011, geodetic measurements determined that the Earth had shrunk by 1 meter in diameter, as the Pacific Plate subducted. Assume the Earth to be a perfect, uniform sphere. Did the Earth’s rotational period change? If so, by how much? All the numbers you need are in the textbook, and you can consider this to be a one-significant-figure problem.

Answer 1

For a sphere of mass M and radius R, moment of inertia of the sphere is given by

The earth takes 24 hr to complete one revolution.

So, angular velocity of earth is

If after shrinking, the new radius be R', we must have by the principle of conservation of angular momentum

It is given that after the earthquake the diameter shrank by 1 m

Diameter of earth is 12742 km and after earthquake it became 12741 km

So, ratio of the radius is also equal to the ratio of the diameters and we can write

So the new time period became,

So, the rotational period of earth increased.