Weight of a body is maximum at

Correct Option: Poles of earth

The weight of a body of mass $m$ is the gravitational force acting on it, which is given by the formula:
$W=mg$
where $g$ is the acceleration due to gravity. Since the mass $m$ of a body remains constant everywhere, the weight of the body depends directly on the value of $g$ at that location.

The value of $g$ on the Earth's surface is not uniform and varies due to two primary reasons:

1. Shape of the Earth:
The Earth is not a perfect sphere but an oblate spheroid. It is flattened at the poles and bulges at the equator. Consequently, the polar radius ($R_p$) is about 21 km shorter than the equatorial radius ($R_e$). Since the acceleration due to gravity is inversely proportional to the square of the Earth's radius:
$g=\frac{GM}{R^2}$
a smaller radius at the poles results in a stronger gravitational pull, making $g$ maximum at the poles and minimum at the equator.

2. Rotation of the Earth:
The rotation of the Earth produces a centrifugal force acting outwards, which opposes gravity. This centrifugal force is maximum at the equator and decreases to zero at the poles. The effective value of gravity at latitude $\theta$ is given by:
$g^{\prime }=g-{\omega }^{2}R{\cos }^2\theta$
At the poles ($\theta =90°$), the term $\cos \theta =0$, meaning there is no centrifugal reduction, and the acceleration due to gravity remains at its maximum value.

Therefore, because the acceleration due to gravity ($g$) is greatest at the poles, the weight of a body is also maximum at the poles of earth.