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Gravitational force is a natural phenomenon by which bodies with mass attract each other. On Earth, it gives us weight and holds everything down. Santa's weight at the North Pole is essentially the gravitational force acting on him at that point. This force is measured using a spring balance that reads 875 N. The gravitational force can be calculated using the formula: \[ W = mg \]where:- \( W \) is the weight,- \( m \) is mass, and- \( g \) is the gravitational acceleration (approximately 9.81 m/s² near the Earth's surface). This formula shows that weight depends on both mass and gravitational acceleration. At any location on Earth, you can determine the weight of an object by multiplying its mass by the gravitational acceleration at that point.

Centrifugal force is an apparent force that acts outward on a body moving around a center, arising from the body's inertia. At the Earth's equator, this force affects how weight is perceived because it reduces the gravitational force slightly due to the Earth's rotation.In mathematical terms, centrifugal force is given by:\[ F_c = m \omega^2 R \]where:- \( F_c \) is the centrifugal force,- \( m \) is the mass,- \( \omega \) is the angular velocity of Earth's rotation,- \( R \) is Earth's radius.At the equator, the centrifugal force due to Earth's rotation decreases the effective gravitational force felt by Santa. This means that if Santa stands on a spring balance at the equator, his weight reading will be less compared to the North Pole.

Weight calculation involves determining how much gravitational force acts upon a mass. For Santa, whose weight at the North Pole is already known to be 875 N, we are interested in finding how this value changes at the equator. To find Santa's mass, we rearrange the weight formula:\[ m = \frac{W}{g} \]where:- \( W \) is the weight at the North Pole,- \( g \) is the gravitational acceleration.Once the mass is determined, Santa's weight at the equator is found by calculating the effective gravitational force:\[ W_{equator} = m \cdot g_{eff} \]where \( g_{eff} \) is the effective gravitational acceleration at the equator, accounting for both gravity and the reduced effect due to centrifugal force. This involves subtracting the centrifugal effect from the standard gravitational acceleration.

Earth's rotation has a subtle but significant effect on how we perceive weight. As the Earth spins, objects at the equator experience a centrifugal force, which effectively reduces the gravitational pull experienced on its surface.This effect can be described in terms of effective gravity:\[ g_{eff} = g - \omega^2 R \]where:- \( g \) is the acceleration due to gravity,- \( \omega \) is Earth's angular velocity,- \( R \) is the radius of the Earth.By subtracting the centrifugal acceleration from the gravitational acceleration, we find the effective gravity at the equator, \( g_{eff} \). This adjustment is necessary for accurate weight measurements at different latitudes, demonstrating how the Earth's rotation tangibly influences physical measurements.