TPR FL #1 C/P Question #4

[poochimaster]

Hello,

I always struggle with questions that ask 'which of the following could also be units for variable x'. In the passage, they tell you that the units of the surface tension coefficient is N/m and ask you what else it could be. Here is the question and solution:

Now I completely understand the explanation given, but while I was doing the test I wouldn't have ever come up with that solution or it would've taken me forever to do. Do you guys have any tips on how to do these types of problems quickly and accurately?

Thank you!

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[Formation]

The best way to do is to just go through the answer choices.

You're given the units N/m to start with. The very first thing you do in this sort of question is write everything in its SI base units. m is already a base unit, so you'll want to convert N.

That isn't something you'll have to necessarily memorize, you can figure out from the equations. N is a unit of Force, which has the equation F = ma. Units for m (mass) are kg, and units for a (acceleration) are m/s^2, which means that N in base units is kg*m/s^2. Put that back into the units for surface tension and you get kg*m/s^2/m, or simply kg/s^2. You can confidently eliminate option A.

Option B involves W (watts), units for Power. So let's write that in SI base units. The power equation is P = W/t, which would give you units of J/s. How about J? Joules are units of energy or work, which has the equation W = Fd, giving you units of N*m. Put that into the units for power, and you now have N*m/s. Option B suggests dividing watts by s^2, which would give you N*m/s^2, which isn't N/m, so you can confidently eliminate that.

Option C involves Newtons. We're already given that the units for surface tension are N/m, so anything else involving newtons that isn't N/m is clearly wrong. So you can confidently eliminate that one too.

That leaves you with option D. To check that answer, we already know that J can be written as N*m. Divide that by m^2, and you're left with N/m, which is exactly what the units for surface tension are.

In practice, given that you know the equations, if you go through the options like this you'll be able to do a problem like this very quickly and be very confident in your answer.