Calculate the angular speed of rotation of the Earth so that the apparent g at the equator becomes half of its value at the surface. Also calculate the length of the day in this situation.

Explanation

To solve the problem of calculating the angular speed of rotation of the Earth so that the apparent gravitational acceleration at the equator becomes half of its value at the surface, we can follow these steps:

### Step 1: Understand the relationship between gravitational acceleration and apparent gravitational acceleration
At the equator, the apparent gravitational acceleration (\(g'\)) is given by the formula:
\[ g' = g - \omega^2 R \]
where:
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