Inertia is a property of matter that describes its resistance to changes in motion. The mass of an object is directly proportional to its inertia, meaning that objects with greater mass have greater inertia. In this case, both the 1 kg of cotton and the 1 kg of iron have the same mass, so they also have the same inertia. This is because mass is the measure of the amount of matter in an object, regardless of the material it is made of.
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Inertia depends on mass, not material composition. Both 1 kg of cotton and 1 kg of iron have the same mass, hence they exhibit the same inertia. Inertia is a property that describes an object's resistance to changes in its state of motion, which is solely determined by its mass.
1 kg of iron is heavier than 1 kg of cotton because the weight is determined by the mass of the object, not the material it is made of.
Both cotton and iron will weigh the same in a vacuum because weight is determined by the mass of an object and gravity. Each object weighs 1 kg in this scenario, regardless of the environment.
Both the cotton and iron will fall to the ground at the same rate because in the absence of air resistance, all objects fall at the same rate regardless of their mass. This phenomenon is known as the Equivalence Principle.
When we say that 1 kg of iron / cotton, we mean that it is the apparent weight. As they are already displacing air and by Archimedes' Principle they both are acted upon by the buoyant force directly proportional to the weight of air they displaced, and cotton displaces more air, therefore its actual weight is more than actual weight of iron.
In vacuum, both 1 kg of cotton and 1 kg of iron would weigh the same. Weight is the force exerted by gravity on an object, and in vacuum, there is no air resistance or buoyancy affecting the weight of the objects. So, 1 kg of cotton and 1 kg of iron would have the same weight.