What should be the period of rotation of earth so as to make any object on the equator weig half of its present value?

Explanation

To find the period of rotation of the Earth so that an object at the equator weighs half of its present value, we can follow these steps:

### Step 1: Understand the forces acting on the object
At the equator, the weight of the object (mg) acts downward, while the centrifugal force due to the Earth's rotation acts outward. The effective weight (apparent weight) can be expressed as:
\[ W' = mg - m\omega^2 r \]
where:
- \( W' \) is the apparent weight,
- \( m \) is the mass of the object,
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