At which location on the Earth would the weight of an object be greatest due to gravitational force?

Introduction / Context:
Weight is the force with which the Earth attracts a body towards its centre and is given by the product of mass and local gravitational acceleration. However, the value of gravitational acceleration is not uniform over the surface of the Earth. It varies slightly with latitude due to the planet's rotation and its equatorial bulge. This question asks you to identify the location where an object would weigh the most, which is a classic concept in physics based geography and physical science sections of competitive exams.

Given Data / Assumptions:

• Weight depends on gravitational acceleration at a particular location.
• The Earth is slightly flattened at the poles and bulging at the equator, not a perfect sphere.
• The options specify locations: equator, surface of the Earth (general), centre of the Earth and poles of the Earth.
• We assume standard conditions without extra forces other than gravity and rotation.

Concept / Approach:
The effective gravity on the Earth's surface is influenced by two main factors: the distance from the centre of the Earth and the centrifugal force due to rotation. At the equator, the centrifugal force is maximum and the radius of the Earth is slightly larger because of the equatorial bulge. This decreases effective gravity. At the poles, the centrifugal force is minimum (almost zero) and the distance to the centre is slightly less, so gravitational acceleration is slightly higher. At the centre of the Earth, gravitational forces from all directions cancel, leading to zero net gravity. Therefore, the weight of an object is greatest at the poles and smallest at the centre, with intermediate values elsewhere on the surface.

Step-by-Step Solution:
Step 1: Recall that weight W is given by W = m * g, where m is mass and g is local gravitational acceleration. Step 2: Recognise that g varies slightly with latitude because of the Earth's rotation and shape. Step 3: At the equator, centrifugal force due to rotation is greatest and the radius is larger, both of which slightly reduce g. Step 4: At the poles, centrifugal force is minimal and the radius is slightly smaller, increasing g compared to the equator. Step 5: Therefore, for the same mass, weight is highest at the poles, making the poles the location where an object would weigh the most.

Verification / Alternative Check:
Textbooks and standard references often provide approximate values of g, showing it to be about 9.78 m/s^2 at the equator and about 9.83 m/s^2 at the poles. These values confirm that gravitational acceleration is slightly larger at the poles. At the centre of the Earth, by symmetry, gravitational attraction from all sides cancels, making g effectively zero. Since weight is proportional to g, any increase in g translates directly into increased weight for the same mass. This numerical check strongly supports the conclusion that weight is maximum at the poles.

Why Other Options Are Wrong:
On the equator, the combined effects of greater radius and maximum centrifugal force reduce effective gravity slightly, so weight there is less than at the poles. The option on the surface of the earth is too vague and does not specify location, but overall maximum weight occurs at the poles, not uniformly everywhere. At the centre of the earth, gravitational acceleration is zero, so the weight of an object would also be zero, which is the opposite of maximum weight. Thus, the equator, centre and generic surface options do not represent the point of greatest weight.

Common Pitfalls:
A common mistake is assuming that weight is highest at the equator because that is where the gravitational force is mistakenly thought to act most directly. Another error is to ignore the effect of rotation and think that gravity is the same everywhere on the surface. Students may also misinterpret the phrase surface of the earth as implying maximum weight, without considering variations. To avoid these issues, remember that both the shape of the Earth and its rotation influence gravity and that poles, with minimum centrifugal effect and slightly smaller radius, experience slightly higher g and hence higher weight.

Final Answer:
The weight of an object is greatest on the poles of the earth, so that is the correct option.