If the radius of the earth contracts to half of its present value without change in its mass, what will be the new duration of the day?

Explanation

To solve the problem, we need to analyze the relationship between the angular momentum of the Earth and its rotational period when the radius changes. Here’s a step-by-step breakdown of the solution:

### Step 1: Understand the Initial Conditions
- Let the mass of the Earth be \( M \).
- Let the initial radius of the Earth be \( R \).
- The initial duration of the day (time period) is \( T \).

### Step 2: Calculate the Initial Angular Momentum
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