Find the imaginary angular velocity of the earth for which the effective acceleration due to gravity at the equator shall be zero. (take `g = 10 m//s^(2)` for the acceleration due to gravity, if the earth were at rest and radius of earth equal to 6400 km and `phi = 60^(@)`)

Explanation

To find the imaginary angular velocity of the Earth for which the effective acceleration due to gravity at the equator becomes zero, we can follow these steps:

### Step 1: Understand the Effective Acceleration Due to Gravity
The effective acceleration due to gravity (\(g'\)) at the equator when the Earth is rotating is given by the formula:
\[ g' = g - \omega^2 R \cos^2 \phi \]
where:
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