Question Video: Understanding the Difference between Fundamental and Derived Quantities | Nagwa Question Video: Understanding the Difference between Fundamental and Derived Quantities | Nagwa

Question Video: Understanding the Difference between Fundamental and Derived Quantities Physics • First Year of Secondary School

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Which of the following most correctly describes the difference between fundamental and derived physical quantities? [A] Derived quantities can have more than one unit, but fundamental quantities can only have one unit. [B] Fundamental quantities can have more than one unit, but derived quantities can only have one unit. [C] Fundamental quantities can be defined in terms of derived quantities. [D] Derived quantities can be defined in terms of fundamental quantities. [E] Fundamental quantities were proposed before derived quantities were proposed.

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Video Transcript

Which of the following most correctly describes the difference between fundamental and derived physical quantities? (A) Derived quantities can have more than one unit, but fundamental quantities can only have one unit. (B) Fundamental quantities can have more than one unit, but derived quantities can only have one unit. (C) Fundamental quantities can be defined in terms of derived quantities. (D) Derived quantities can be defined in terms of fundamental quantities. (E) Fundamental quantities were proposed before derived quantities were proposed.

In this question, we are being asked about the difference between physical quantities that are fundamental quantities and those that are derived quantities. Let’s recall that a fundamental quantity is a quantity that cannot be separated into more fundamental or basic parts. So, for example, length and time are both examples of fundamental quantities. In contrast to this, any quantity that can be separated into more fundamental parts and therefore is not a fundamental quantity is known as a derived quantity.

The statement in option (A) claims that derived quantities can have more than one unit, but fundamental quantities can only have one unit. Now we’ve just said that time is an example of a fundamental quantity. And let’s recall that some units we can use to measure time include seconds, minutes, hours, days, and years. Since time is a fundamental quantity and we’ve just seen that it can be measured in a variety of units, then it can’t be true that fundamental quantities can only have one unit. We know then that the second half of the statement in option (A) is definitely wrong. And so option (A) cannot be our answer.

Now, let’s move on to the statement in option (B), which says, “Fundamental quantities can have more than one unit, but derived quantities can only have one unit.” We’ve already seen that fundamental quantities can have more than one unit. So this first half of the statement looks good. However, the second half of the statement claims that derived quantities can only have one unit. Let’s recall that speed is an example of a derived quantity. Some examples of units we can use to measure speed include meters per second, kilometers per hour, and miles per hour. This means that the statement that derived quantities can only have one unit can’t be true, and so the statement in option (B) cannot be correct. Now that we’ve eliminated these first two answer options, let’s clear them off the board to make ourselves some space.

Now, let’s consider the statements in options (C) and (D). Option (C) says fundamental quantities can be defined in terms of derived quantities, while option (D) says derived quantities can be defined in terms of fundamental quantities. Now, fundamental quantities and derived quantities can each be expressed in terms of each other. For example, the derived quantity speed is the distance moved by an object per unit of time. So this derived quantity speed can be expressed in terms of fundamental quantities as the fundamental quantity length divided by the fundamental quantity time. This equation can be rearranged to say that time is equal to length divided by speed.

So now we’ve got a fundamental quantity, time, expressed in terms of a fundamental quantity, length, and a derived quantity, speed. However, since speed itself is obtained from the quantities length and time, then expressing the quantity time in terms of length and speed is really just saying that time is equal to length divided by length divided by time. Now on the right-hand side, length divided by length over time is just the same as length multiplied by time over length. We can then slightly rearrange the way that we’ve written things on the right-hand side here. So the equation now reads time is equal to length divided by length multiplied by time. Since length divided by length is simply equal to one, then this term cancels out. And then we’re just left with the somewhat circular and not particularly enlightening statement that time is equal to time.

So we’ve seen through this example equation here that derived quantities can indeed be defined in terms of fundamental quantities. We’ve also seen an example in this equation here of how it’s possible to express a fundamental quantity in terms of other fundamental and derived quantities. However, since the derived quantity, which in this case is speed on the right-hand side, can itself be defined in terms of fundamental quantities, in this case length and time, then this equation isn’t really defining the fundamental quantity time in terms of derived quantities. It’s basically just a more convoluted way of making the circular statement that time is equal to time.

So while the statement in option (D) that derived quantities can be defined in terms of fundamental quantities is a correct statement, it’s not really so true to say that fundamental quantities can be defined in terms of derived quantities, which is the statement in option (C). Let’s eliminate option (C) then. And at this stage it looks like option (D) may well be our answer.

To be sure of this, though, we should also check out the statement in option (E), which says that fundamental quantities were proposed before derived quantities were proposed. Now a lot of these physical quantities were proposed a really long time ago. For example, the idea of length, time, and speed being measurable quantities is so old that it’s really not known when the idea first appeared. This means that we don’t really have any way of knowing whether or not it’s the case that fundamental quantities were proposed before derived quantities. So then whether or not this statement in option (E) happens to be true, which really isn’t something that we can know for sure, it certainly isn’t the defining difference between fundamental and derived physical quantities.

This means we can safely eliminate option (E). This leaves us with our answer as the statement in option (D). The most correct way to describe the difference between fundamental and derived physical quantities is to say that derived quantities can be defined in terms of fundamental quantities.

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