New earth, How does it look like?

Classical Mechanics Level 5

A meteor strikes the earth,well ... as a natural consequence, humanity has vanished as any other kind of life ,the meteor was as big as a mercury, after 8 years the new earth started to cool down and take another spherical shape, well not exactly as a perfect sphere It's shape is as oblate spheroid.

What is the pole to pole diameter of the new earth?

Details And Assumptions:

-The meteor has increased the mass of Earth.

-The meteor-Earth mixed new planet is homogeneous.

-The angular velocity of the new Earth is \( \omega =2\pi \text{rad/day}\).

-The new equatorial radius is 7530 km.

-New mass of the earth is \(\frac{1}{6.67}10^{26}Kg \).

Hint: What is the condition so masses aren't displaced to another location on the New Earth?

express your answer in Kilometer with three decimal places.


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