Concept notes: The concept of mass and weight is fundamental in understanding physical properties. Mass is a measure of the amount of matter in an object, and it remains constant regardless of the object's location. Weight, on the other hand, is the force exerted on an object due to gravity and can vary depending on the gravitational field strength. In this context, 1 kg of iron and 1 kg of cotton have the same mass, and thus the same weight on Earth.
Explanation: The concept of mass and weight is crucial in understanding the physical properties of materials. Mass is a fundamental property of matter that quantifies the amount of matter in an object. It is measured in kilograms (kg) and is a scalar quantity, meaning it has magnitude but no direction. The mass of an object remains constant regardless of its location in the universe.
Weight, on the other hand, is the force exerted on an object due to gravity. It is a vector quantity, meaning it has both magnitude and direction. Weight is measured in newtons (N) and is calculated using the formula \( W = m \times g \), where \( W \) is the weight, \( m \) is the mass, and \( g \) is the acceleration due to gravity. On Earth, the acceleration due to gravity is approximately \( 9.8 \, \text{m/s}^2 \).
In the context of the question, both iron and cotton have the same mass of 1 kg. Therefore, their weights on Earth are also the same, as the gravitational force acting on them is the same. The misconception that iron is heavier than cotton arises from the fact that iron has a higher density than cotton. Density is defined as the mass per unit volume of a substance and is calculated using the formula \( \rho = \frac{m}{V} \), where \( \rho \) is the density, \( m \) is the mass, and \( V \) is the volume. Iron has a higher density than cotton, which means that a given volume of iron will have more mass than the same volume of cotton. However, when the mass is the same, the weight is also the same, regardless of the material.
In summary, 1 kg of iron and 1 kg of cotton have the same mass and, consequently, the same weight on Earth. The correct answer is that they are equal in weight, as mass is a measure of the amount of matter in an object and is independent of the material's density.