If earth suddenly contracts to half of its present radius keeping its mass constant what would be the length of the day?

Explanation

To solve the problem of determining the new length of the day if the Earth suddenly contracts to half of its present radius while keeping its mass constant, we can use the principle of conservation of angular momentum. Here’s a step-by-step solution:

### Step 1: Understand the concept of angular momentum
Angular momentum (L) is conserved in a closed system. For a rotating body, it can be expressed as:
\[ L = I \omega \]
where \( I \) is the moment of inertia and \( \omega \) is the angular velocity.

### Step 2: Define the initial and final states
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