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The Earth was formed about 4.5 billion years ago, probably as a sphere of roughly uniform density. Shortly thereafter, heat from the decay of radioactive elements caused much of the Earth to melt. This allowed the heavier material to sink to- ward the center of the Earth, forming the core. Today, we can picture the Earth as made up of a core of radius 3570 km and density 10.3 g/cm 3 surrounded by a mantle of density 4.50 g/cm 3 extending to the surface of the Earth (radius 6370 km). We ignore the crust of the Earth. Calculate the fractional change in the length of the day due to the formation of the core.

The Earth was formed about 4.5 billion years ago, probably as a sphere of roughly uniform density. Shortly thereafter, heat from the decay of radioactive elements caused much of the Earth to melt. This allowed the heavier material to sink to- ward the center of the Earth, forming the core. Today, we can picture the Earth as made up of a core of radius 3570 km and density 10.3 g/cm3 surrounded by a mantle of density 4.50 g/cm3 extending to the surface of the Earth (radius 6370 km). We ignore the crust of the Earth. Calculate the fractional change in the length of the day due to the formation of the core.

Grade:upto college level

1 Answers

Navjyot Kalra
askIITians Faculty 654 Points
8 years ago
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The negative value of change in length of day over the initial length depicts the fact that the final rotational inertia of the Earth was smaller than the initial rotational inertia. Therefore, the Earth would spin faster when the core is formed, and the length of the day will decrease.

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