If earth contracts to half of its present radius what would be the length of the day at equator ?

Explanation

To solve the problem of determining the length of the day at the equator if the Earth contracts to half of its present radius, we can follow these steps:

### Step 1: Understand the Concept of Angular Momentum
Angular momentum (L) is conserved in a closed system where no external torque acts. The angular momentum is given by the formula:
\[ L = I \cdot \omega \]
where \( I \) is the moment of inertia and \( \omega \) is the angular velocity.

### Step 2: Calculate the Moment of Inertia for the Earth
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