How much decrease will occur in duration of day if earth contracts to one third of its present radius?

Explanation

To solve the problem of how much the duration of a day will decrease if the Earth contracts to one third of its present radius, we can follow these steps:

### Step 1: Understand the Concept of Angular Momentum
Since there is no external torque acting on the Earth, we can use the principle of conservation of angular momentum. The angular momentum \( L \) of a rotating body is given by:
\[ L = I \cdot \omega \]
where \( I \) is the moment of inertia and \( \omega \) is the angular velocity.

### Step 2: Define the Initial and Final Conditions
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