Suppose the earth increases it speed of rotation. At what new time period will the weight of a body on the equator becomes zero ? (Take, `g = 10 ms^(-2)` and radius of earth R = 6400 km)

Explanation

To solve the problem, we need to find the new time period (T) at which the weight of a body on the equator becomes zero when the Earth increases its speed of rotation.

### Step-by-Step Solution:

1. **Understanding the Condition for Weight to be Zero:**
The weight of a body becomes zero when the centrifugal force due to the Earth's rotation equals the gravitational force acting on the body. The centrifugal force can be expressed as \( F_c = m \omega^2 R \), where \( m \) is the mass of the body, \( \omega \) is the angular velocity, and \( R \) is the radius of the Earth.

2. **Gravitational Force:**
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