Variation in the Value of ‘g’ (Acceleration due to Gravity)

The value of acceleration due to gravity, represented by ‘g,’ is a fundamental concept in physics that plays a crucial role in various scientific applications.

However, it is not a constant value across the Earth’s surface; it varies based on several factors such as altitude, latitude, and the Earth’s rotation.

In this post, we will explore the factors that lead to variations in the value of ‘g.’

🔰 Explore Comprehensive General Science Notes on Physics

Variation with Height and Depth

The value of ‘g’ changes as we move away from or closer to the Earth’s surface.

With Height

• The distance from the Earth’s center increases as you move to higher altitudes (for example, climbing a mountain or flying in an airplane).

• This causes the gravitational pull to decrease. The formula for the variation of gravity with height is:

Where:

• g_h​ is the acceleration due to gravity at height h.
• g₀​ is the acceleration due to gravity at the Earth’s surface.
• h is the height above the Earth’s surface.
• R is the Earth’s radius.

Hence, the higher you go, the weaker the pull of gravity. For instance, the value of ‘g’ at the top of Mount Everest is slightly less than the value at sea level.

With Depth

• On the other hand, as we go deeper below the Earth’s surface, the value of ‘g’ also decreases.

• At the Earth’s core, the value of gravity theoretically becomes zero, as there is an equal amount of mass pulling in all directions.

• The formula for gravity at a depth dd below the Earth’s surface is:

Where:

• g_d is the acceleration due to gravity at depth d.
• g₀ is the acceleration due to gravity at the surface.

This decrease is because the mass of the Earth beneath you contributes less to the gravitational pull as you go deeper into the Earth.

Variation with Latitude: Poles vs. Equator

The value of ‘g’ also varies with latitude, meaning that the acceleration due to gravity is different at different points on the Earth’s surface.

At the Poles

• Gravity is maximum at the poles. This is because the Earth is not a perfect sphere but rather an oblate spheroid (flattened at the poles and bulging at the equator).

• The Earth’s rotation causes a centrifugal force that slightly counteracts gravity.

• At the poles, this effect is absent, so the full force of gravity is experienced. Therefore, the value of ‘g’ is higher at the poles.

At the Equator

• Gravity is minimum at the equator. The Earth’s rotation creates a centrifugal force that partially opposes the force of gravity.

• The centrifugal force is maximum at the equator due to the Earth’s rotational speed.

• This reduces the effective gravitational pull at the equator. Hence, the value of ‘g’ is slightly lower at the equator compared to the poles.

Effect of Earth’s Rotation on ‘g’

The Earth’s rotation has a significant effect on the value of ‘g’ experienced at its surface. As mentioned earlier, the centrifugal force due to Earth’s rotation reduces the effective value of gravity. The effect is more pronounced at the equator and diminishes towards the poles.

Increased Rotation (Angular Speed)

• If the angular speed of Earth’s rotation increases (for example, if the Earth were to spin faster), the centrifugal force would become stronger.

• This would further reduce the value of gravity, especially at the equator.

• If the Earth’s rotation speed increases drastically, it could lead to a noticeable reduction in the perceived gravitational pull.

Decreased Rotation (Angular Speed)

• On the other hand, if the Earth’s rotation slows down, the centrifugal force would decrease, and gravity would increase.

• This is because the Earth would exert a stronger gravitational force without the opposing effect of the centrifugal force.

• If the Earth were to stop rotating entirely, the only force acting would be gravitational, and the value of ‘g’ at the equator would become the same as at the poles.

Summary of Factors Affecting the Value of ‘g’

• Height above the Earth’s surface: As you go higher, ‘g’ decreases.
• Depth below the Earth’s surface: As you go deeper, ‘g’ decreases.
• Latitude: Gravity is maximum at the poles and minimum at the equator.
• Rotation of Earth: Gravity is weaker due to the centrifugal force created by the Earth’s rotation, particularly at the equator.

In conclusion, the value of ‘g’ is not a fixed number but varies based on location, altitude, and the Earth’s rotation. Understanding these variations is crucial in fields such as physics, engineering, and geophysics.

Related Posts: