If the rotational speed of earth increase, then weight of body at the equator

Options

A. Increases
B. Decreases
C. No effect
D. Becomes double

Explanation

To solve the problem of how the weight of a body at the equator changes if the rotational speed of the Earth increases, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding Weight and Forces**:
- The weight of a body is given by the formula \( W = mg \), where \( m \) is the mass of the body and \( g \) is the acceleration due to gravity.

2. **Identifying Forces at the Equator**:
- At the equator, a body experiences two forces:
- The gravitational force acting downward, which is \( mg \).
- The centripetal force due to the Earth's rotation, which acts outward and is given by \( F_c = m \omega^2 r \), where \( \omega \) is the angular velocity of the Earth and \( r \) is the radius of the Earth.

3. **Effective Gravitational Acceleration**:
- The effective gravitational acceleration \( g' \) at the equator can be expressed as:
\[ g' = g - \omega^2 r \]
- Here, \( g' \) is the effective gravitational acceleration that a body experiences due to the combined effects of gravity and the outward force due to rotation.

4. **Effect of Increasing Rotational Speed**:
- If the rotational speed of the Earth increases, this means that \( \omega \) increases. Consequently, the term \( \omega^2 r \) also increases.
- As \( \omega^2 r \) increases, the effective gravitational acceleration \( g' \) decreases because it is being subtracted from \( g \).

5. **Conclusion on Weight**:
- Since the effective gravitational acceleration \( g' \) decreases with an increase in rotational speed, the weight of the body, which is given by \( W' = mg' \), will also decrease.
- Therefore, if the rotational speed of the Earth increases, the weight of a body at the equator decreases.

### Final Answer:
The weight of a body at the equator decreases if the rotational speed of the Earth increases.

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