What is the relationship between mass and weight?

What is the relationship between mass and weight?

• A. Mass is equal to weight.
• B. Mass is proportional to weight; as mass changes, weight changes at a constant rate.
• C. Mass increases weight independently of gravity.
• D. Mass and weight are unrelated.

Answer: (B)

Weight is the gravitational force acting on a mass, while mass is the amount of matter in an object. The relationship between them is given by W = m g, where g is the gravitational acceleration. Since g is essentially constant near Earth’s surface, weight changes in direct proportion to mass: doubling the mass doubles the weight. The rate of change of weight with respect to mass is g, a constant for a given location. If you were on a different planet or at a different altitude where gravity differs, the proportionality still holds, but the constant g would be different, so the same mass would weigh more or less accordingly. This is why mass is proportional to weight with a constant rate of change, rather than being equal or completely unrelated.

Weight is the gravitational force acting on a mass, while mass is the amount of matter in an object. The relationship between them is given by W = m g, where g is the gravitational acceleration. Since g is essentially constant near Earth’s surface, weight changes in direct proportion to mass: doubling the mass doubles the weight. The rate of change of weight with respect to mass is g, a constant for a given location. If you were on a different planet or at a different altitude where gravity differs, the proportionality still holds, but the constant g would be different, so the same mass would weigh more or less accordingly. This is why mass is proportional to weight with a constant rate of change, rather than being equal or completely unrelated.