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Question Video: Understanding the Definition of the Kilogram Physics

What of the following features of the International Prototype of the Kilogram are directly relevant to what the prototype of the kilogram has been made to do? [A] Its shape [B] Its volume [C] Its mass [D] How much time it has existed for

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Video Transcript

What of the following features of the International Prototype of the Kilogram are directly relevant to what the prototype of the kilogram has been made to do? (A) Its shape, (B) its volume, (C) its mass, (D) how much time it has existed for.

Let’s begin by recalling that the International Prototype of the Kilogram was created as a means of defining the SI base unit of kilograms. We can further recall that the kilogram is the SI base unit of the quantity mass. So the International Prototype of the Kilogram was an object designed to have a mass of exactly one kilogram. And it provides the standard reference for what a mass of one kilogram is. Clearly then, the mass of the International Prototype of the Kilogram is directly relevant to what it was made to do. This feature of the international prototype is the one listed in option (C). So we know that answer option (C) is a relevant feature.

Let’s now check out the three remaining options to see if any of these are relevant as well. Option (B) lists the feature of volume. However, it’s perfectly possible for two objects with different volumes to have the same value of the physical quantity mass. This is because the two objects could be made of materials that have different densities, where we can recall that the density of an object is equal to the object’s mass divided by its volume. So then, since we could have two objects with different volumes but each with the same mass of one kilogram, then the feature of volume can’t be directly relevant to the International Prototype of the Kilogram. This means that we can eliminate answer option (B).

We can use a similar kind of reasoning for answer option (A), which claims that the shape of the International Prototype of the Kilogram could be directly relevant to what it was made to do. Just as we can have two objects with different volumes that both have the same mass of one kilogram, we can also have objects that have different shapes that still have this same mass of one kilogram. In fact, technically, this International Prototype of the Kilogram could have any kind of shape, although admittedly some shapes are probably more practical than others to create, to precise specifications of mass. While the shape of the object might affect some practical considerations though, it’s in no way directly relevant to what the International Prototype of the Kilogram was made to do, which is to define the SI base unit of mass. This means that we can eliminate answer option (A).

Lastly, let’s take a look at answer option (D), which claims that how much time it has existed for could be a directly relevant feature of what the prototype of the kilogram was made to do. Recalling once more that the International Prototype of the Kilogram was made to define the SI base unit of mass, we should be able to see that the length of time that the prototype has existed for has no relevance to this.

Experience should tell us that the mass of an object does not change as more time passes. For example, if we go into a gym one day and load up a weights bar with 20-kilogram plates, then whatever day we chose to visit the gym, we would always expect those plates to have the same mass of 20 kilograms. So if we went back a week later, say, and we loaded up the same bar with the same two 20-kilogram plates, we would know that the total mass would be the same. We can see then that the amount of time that the International Prototype of the Kilogram has existed for can be in no way directly relevant to what it was made to do, which is to define the SI base unit of mass. This means that we can eliminate answer option (D).

This just leaves us then with answer option (C). The only one of the given features of the International Prototype of the Kilogram which is directly relevant to what it was made to do is its mass.

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