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Chapter 6: Problem 683

As we go from the equator to the poles, the value of \(g \ldots \ldots \ldots\) (A) Remains constant (B) Decreases (C) Increases (D) Decreases upto latitude of \(45^{\circ}\)

Short Answer

Expert verified
As we move from the equator to the poles, the value of gravity (\(g\)) increases. This is because the Earth's radius decreases with increasing latitude, causing an increase in the radial gravitational force, while the centrifugal force decreases. Therefore, the net effect is an increase in the gravitational force experienced by an object as it goes from the equator towards the poles.

Step by step solution

01

- Recap the equation of gravity and its components

Gravity is the force with which the Earth attracts objects towards its center. It has two components: radial gravity and centrifugal force. The radial gravity is the force that pulls objects directly towards the Earth's center, while the centrifugal force is the force that acts on objects in a rotating frame, such as Earth. The overall gravity (g) can be expressed as the difference between the radial gravity and the centrifugal force. This difference will determine how the value of gravity changes with latitude.
02

- Discuss the difference in Earth's radius and gravitational force between the equator and poles

The Earth is not a perfect sphere, but rather an oblate spheroid. This means the Earth's radius is larger at the equator and smaller at the poles due to its rotation. As a result, objects on the Earth experience more radial gravity at the poles, while objects at the equator experience a combination of radial gravity and centrifugal force. To understand how the value of gravity changes with latitude, we need to consider the difference in Earth's radius and the gravitational force acting on an object at different latitudes.
03

- Explain how the value of gravity changes from equator to poles

As we move from the equator towards the poles, the Earth's radius decreases, and the radial gravitational force acting on an object increases. However, the centrifugal force, which acts in the opposite direction of radial gravity, also decreases. This is because as we move from the equator to the pole, the distance from the axis of rotation decreases, reducing the effect of the centrifugal force. So, the net effect is an increase in the overall gravitational force experienced by an object when moving from the equator towards the poles. Based on this understanding, we can now determine which option is correct.
04

- Select the correct option

Considering that the value of gravity increases as we move from the equator to the poles, the correct answer is: (C) Increases

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