If the earth suddenly contracts to one third of its present size, calculate by how much would the day be shortened ?

Explanation

To solve the problem of how much the day would be shortened if the Earth suddenly contracts to one third of its present size, we will follow these steps:

### Step 1: Understand the relationship between angular momentum and moment of inertia
The angular momentum (L) of a rotating body is given by the product of its moment of inertia (I) and angular velocity (ω):
\[ L = I \cdot \omega \]
If the Earth contracts, its moment of inertia changes, but angular momentum is conserved (assuming no external torque).

### Step 2: Define initial and final moments of inertia
...