How is weight mathematically defined?

Weight is mathematically defined as the product of mass and the acceleration due to gravity. This relationship is rooted in Newton's second law of motion, which states that force equals mass times acceleration (F = ma). In the context of weight, the force being referred to is the gravitational force acting on an object. Therefore, weight can be expressed with the formula:

Weight (W) = mass (m) × acceleration due to gravity (g).

Here, the acceleration due to gravity near the Earth's surface is approximately 9.81 m/s². This means that the weight of an object is directly proportional to both its mass and the strength of the gravitational field it is in. This is a fundamental concept in physics, applicable in various scenarios, from calculating the gravitational force on objects to understanding how weight changes with variations in gravitational acceleration, such as on different celestial bodies. Each of the other options does not correctly capture this fundamental relationship between mass and gravitational acceleration as it pertains to weight.