The correct option is **B**: Mass is a scalar quantity that measures the amount of matter, while weight is a vector quantity that measures the force of gravity acting on that mass. ### Detailed Explanation 1. **Understanding Mass**: - **Definition**: Mass is a measure of the amount of matter in an object. It quantifies how much "stuff" is present, regardless of its location in the universe. - **Nature**: Mass is a scalar quantity, which means it has magnitude but no direction. For example, if an object has a mass of 5 kilograms, it simply means it contains that amount of matter, without any directional component. - **Units**: The standard unit of mass in the International System of Units (SI) is the kilogram (kg). 2. **Understanding Weight**: - **Definition**: Weight is the force exerted on an object due to gravity. It is the gravitational pull that the Earth (or another celestial body) exerts on the mass of the object. - **Nature**: Weight is a vector quantity, which means it has both magnitude and direction. The direction of weight is always towards the center of the gravitational body (e.g., Earth). - **Formula**: The weight (W) of an object can be calculated using the formula: \[ W = m \cdot g \] where \( m \) is the mass of the object and \( g \) is the acceleration due to gravity (approximately \( 9.81 \, \text{m/s}^2 \) on Earth). - **Units**: The standard unit of weight in the SI system is the newton (N), which is equivalent to \( \text{kg} \cdot \text{m/s}^2 \). 3. **Key Differences**: - **Dependence on Gravity**: Mass remains constant regardless of location, while weight changes depending on the gravitational field strength. For example, an object with a mass of 10 kg will weigh about 98.1 N on Earth but only about 37.2 N on the Moon, where gravity is weaker. - **Scalar vs. Vector**: Mass is a scalar quantity (no direction), while weight is a vector quantity (has direction). ### Why the Other Options are Incorrect - **Option A**: "Mass is the force exerted on an object due to gravity, while weight is a measure of the amount of matter in an object." - **Incorrect**: This statement reverses the definitions of mass and weight. Mass measures the amount of matter, while weight is the force due to gravity acting on that mass. - **Option C**: "Mass changes with location, while weight remains constant regardless of the gravitational field." - **Incorrect**: This is the opposite of the truth. Mass does not change with location; it is constant. Weight, however, varies with the strength of the gravitational field. - **Option D**: "Mass is measured in newtons, while weight is measured in kilograms." - **Incorrect**: This statement confuses the units. Mass is measured in kilograms (kg), while weight is measured in newtons (N). ### Common Pitfalls - Confusing mass and weight is a common mistake. Remember that mass is about how much matter is present, while weight is about the force of gravity acting on that matter. - Forgetting that weight can change based on location (e.g., on different planets) while mass remains constant. ### Revision Summary - **Mass**: Scalar quantity measuring the amount of matter; constant regardless of location; measured in kilograms (kg). - **Weight**: Vector quantity measuring the force of gravity on mass; varies with gravitational field strength; measured in newtons (N). - **Key Formula**: \( W = m \cdot g \) (Weight = Mass × Acceleration due to gravity). - **Remember**: Mass does not change with location; weight does.