On the Earth, the acceleration due to gravity (gravitational force per unit mass) is maximum at which of the following locations?

Introduction / Context:
The strength of gravity at the Earth's surface, usually represented by g, is not exactly the same everywhere. It varies slightly with latitude and altitude. This question asks where g, and therefore the gravitational force per unit mass, is maximum: at the poles, the equator or intermediate latitudes such as the tropics.

Given Data / Assumptions:

• The Earth is not a perfect sphere; it is slightly flattened at the poles and bulged at the equator (an oblate spheroid).
• The Earth rotates on its axis, creating a centrifugal effect.
• We are comparing surface gravity values at poles, equator and tropical regions.
• We assume the same altitude above sea level for all locations.

Concept / Approach:
Two main factors affect surface gravity with latitude: the Earth's rotation and its shape. At the equator, the centrifugal effect due to rotation is maximum and slightly reduces the effective gravity. In addition, the equatorial bulge means the surface is farther from the Earth's centre, reducing gravitational attraction, which decreases with distance. At the poles there is no centrifugal reduction, and the distance to the centre is slightly smaller, so gravity is strongest there. Between these extremes are the tropics, where values are intermediate.

Step-by-Step Solution:
Step 1: Consider the Earth's shape. It is flattened at the poles and bulged at the equator, so the radius is smallest at the poles. Step 2: Gravity is stronger when you are closer to the Earth's centre, so this shape effect increases g at the poles. Step 3: Consider rotation. At the equator, rotational motion produces a centrifugal effect that effectively reduces weight slightly. Step 4: At the poles, the axis of rotation passes through the location, so there is no circular motion around the axis and essentially no centrifugal reduction. Step 5: Combining both effects, g is maximum at the poles, lower at mid latitudes and minimum at the equator.

Verification / Alternative check:
Precise measurements show g ≈ 9.78 m/s^2 at the equator and g ≈ 9.83 m/s^2 at the poles. These confirmed values match the theoretical reasoning: the poles have slightly higher gravity. The Tropic of Cancer and Tropic of Capricorn lie between equator and poles, so their g values are intermediate. Therefore, among the options given, the poles clearly correspond to maximum gravitational force per unit mass.

Why Other Options Are Wrong:
The Tropic of Cancer and the Tropic of Capricorn: These latitudes are neither closest to the centre of the Earth nor free of centrifugal reduction; their g values are between equator and poles.

The equator: Here the Earth's radius is largest and centrifugal effect is strongest, making gravity slightly weaker rather than stronger.

Common Pitfalls:
Some learners assume gravity must be greatest at the equator because they think of the Earth as a perfect sphere or confuse centrifugal force direction. Others forget the role of shape and only think about rotation. A helpful summary is: smaller radius and no centrifugal effect at the poles lead to slightly stronger gravity than at the equator or tropics.

Final Answer:
Gravitational force is maximum at the Poles.