Question

Weight of a body is maximum at (A) moon (B) poles of earth (C) Equator of earth (D) Center of earth

Short answer

The weight of a body is maximum at the poles of the earth (B) due to higher gravitational acceleration caused by the Earth's shape (oblate spheroid).

Step-by-step solution

(1) Moon Vs Earth

The gravity of the moon is 1/6th that on the earth, so the weight of a body would be less on the moon compared to anywhere on earth.

(2) Weight at Poles Vs the Equator

The earth's shape (oblate spheroid) causes the weight of a body to vary slightly at different locations. Since the earth is bulging at the equator and flattened at the poles, the weight will be higher at poles due to higher gravitational acceleration.

(3) Weight at Centre of Earth

As we approach the center of the earth, the force exerted within the interior is balanced out by the forces acting from other sides, making gravitational acceleration, and hence the weight, zero at the center of the earth. By comparing these locations, we find that the weight of a body is maximum at the poles of the earth. The correct answer is: (B) poles of earth

Key concepts

Weight Variation on Earth

The weight of an object on Earth is not constant everywhere. Weight is the force of gravity acting on an object, and it changes depending on the location on the Earth's surface. Earth's shape, which is an oblate spheroid, contributes to the variation in gravitational force. This means the distance from the center of the Earth to the surface is slightly shorter at the poles compared to the equator. Since gravitational force depends on this distance, the closer to the Earth's center, the stronger the gravitational pull, and thus, the weight is greater.

• At the equator, the Earth bulges, making the gravitational pull weaker due to the increased distance from the center.
• At the poles, the earth is slightly flattened, making objects heavier because they are closer to the center of Earth.

These differences cause variations in weight at different geographic locations on Earth.

Geographical Variation in Gravity

Gravity on Earth is not uniform and can vary based on geographic location due to the planet's shape and rotation. This geographical variation in gravity affects how objects weigh in different parts of the world.

• Earth's oblate spheroid shape means that the gravitational pull is stronger at the poles and weaker at the equator.
• The centrifugal force due to Earth's rotation slightly counteracts gravity, which is most pronounced at the equator. This makes objects weigh less there compared to the poles.

Therefore, a given object can weigh more at the poles and less at the equator, influencing scientific calculations and measurements.

Earth's Gravitational Field

The Earth's gravitational field is a region where a mass experiences a force due to gravitational attraction. It is strongest at the surface and decreases as you move away from the Earth or towards its center. Understanding this field helps explain why we experience different weights at the Earth's surface.

• The gravitational field is what keeps us anchored to the ground and governs the motion of celestial bodies around the Earth.
• At the Earth's surface, the value of gravitational acceleration, denoted as \( g \), is approximately \( 9.81 \, \text{m/s}^2 \).
• As we go deeper into the Earth, the effective mass pulling an object decreases due to the spherical shell theorem, resulting in no net gravitational force at the Earth's center.

This variability in the gravitational field explains why weight can vary at various points around the Earth.

Gravity on Moon vs. Earth

Gravity significantly differs between the Moon and the Earth. While the Earth provides a strong gravitational pull that keeps us grounded, the Moon's gravity is much weaker.

• The Moon's gravitational force is only about \( \frac{1}{6} \) of Earth's gravity. This means that an object, or a person, would weigh only a fraction of their Earth weight on the Moon.
• This reduced gravity affects how we would move there. For instance, on the Moon, one can jump higher and carry heavier objects with more ease than on Earth due to reduced gravitational pull.
• This difference impacts how space missions are planned and has implications on equipment and human movement on the Moon.

Understanding the contrast in gravity between these celestial bodies is crucial for exploring and utilizing their unique conditions.