Question

What are the physical quantities for the units
A. $mN$
B. $Nm$
C. $nm$

Answer 1

Here, we are given various units, note that these are SI units, you are asked to find which physical quantities do these SI units represent. In order to answer this question, you need to consider each quantity in the units separately and find out what they represent. After knowing that, you combine the units and then determine the physical quantities represented by each unit.

Complete step by step answer:
Let us first consider the option A which has the units as $mN$. Here, there are two quantities which have units $m$ and $N$. The place where the units are kept also has its own importance. Here, capital $N$ is the unit of force and is actually called Newton. The small $m$ here, actually stands for milli. So, the physical quantity in option A is milli Newton.

Now, let us consider option B. Again, we have two physical quantities $m$ and $N$. Here, $N$ is a unit of force and is Newton. But as $m$ is placed after $N$, it denotes the unit of length known as metre. So, the physical quantity in option B is Newton-metre. Now, you know that when we take the cross product of position vector of point of contact of force with force, you get the torque. Therefore, it is the unit of torque.

Finally, in option C, again we have two units $n$ and $m$. As $m$ is placed at the end and not in the first position, it will be metre and as $n$ is placed first, it has to be nano.Therefore, the option C is nanometre.Therefore, $mN$ is milli Newton, $Nm$ is work and $nm$ is nanometre.

Note: You need to focus on the things mentioned in the above solution. You are supposed to determine the physical quantities considering the individual units. You need to keep in mind whether the units given are in small letters or capital letters and also their positions. As you have seen that the small n represents nano whereas capital is Newton and also small m in first position is milli but small m in the end is metre. So, keep these things in mind while determining the physical quantities.