Help with simple dimensional analysis question

In summary, dimensional analysis is a mathematical technique used to convert between units of measurement and check the validity of equations. It is important in ensuring the accuracy and consistency of measurements and calculations, and can be used in any scientific field. To perform simple dimensional analysis, one must identify the dimensions of the quantities involved and use conversion factors or unit equivalences to maintain consistency. Some tips for successfully using dimensional analysis include clearly defining dimensions, using reliable sources, and checking for consistency.
  • #1
budd99
5
0
Which one of the quantities below has dimensions equal to ML/T2

a) mv
b) mv2
c) mv2/r
d) mrv
e) mrv2/r2

I tried splitting it up in M*(L/T)*1/T
which would lead me to mv*T-1 and then I get stuck

Please help!
 
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  • #2
Welcome to Physics Forums :smile:

Since it's multiple choice, how about examining each answer and seeing if it matches ML/T2

For example:

a) mv = M L/T (is not ML/T2)
etc.
 
  • #3
Redbelly98 said:
Welcome to Physics Forums :smile:

Since it's multiple choice, how about examining each answer and seeing if it matches ML/T2

For example:

a) mv = M L/T (is not ML/T2)
etc.

I'm working on it, but what is the r in the answers? Also, why does the m become a capital M?
 
  • #4
For dimensional analysis problems, it's customary to use capital letter M, L and T for Mass, Length, and Time.

r is a distance or length.
 
  • #5
Ok, I think I figured it out...

I took mv2/r

(M(L/T)(L/T))/r

I assumed r = L since both are length measures so...

(M(LL/TT))/L

(M(LL/TTL)

M(L/TT)

M(L/T2)

I don't know if I should be equating r to L though...
 
  • #6
That's correct. Yes, r has dimensions of Length, so use L for its dimension.
 

FAQ: Help with simple dimensional analysis question

What is dimensional analysis?

Dimensional analysis is a mathematical technique used to convert between units of measurement and check the validity of equations. It involves identifying the dimensions of physical quantities and manipulating them to ensure that they are consistent with the units being used.

Why is dimensional analysis important?

Dimensional analysis is important because it allows scientists to ensure the accuracy and consistency of their measurements and calculations. It also helps to identify any errors or inconsistencies in equations or units, which can lead to more accurate and reliable results.

How do I perform simple dimensional analysis?

To perform simple dimensional analysis, you first need to identify the dimensions of the quantities involved in the problem (e.g. length, time, mass). Then, you can use conversion factors or unit equivalences to convert between units and ensure that the dimensions on both sides of the equation are consistent.

Can dimensional analysis be used in any scientific field?

Yes, dimensional analysis can be used in any scientific field where measurements and calculations are involved. It is commonly used in physics, chemistry, and engineering, but can also be applied to other fields such as biology and economics.

What are some tips for successfully using dimensional analysis?

Some tips for successfully using dimensional analysis include: clearly defining the dimensions of all quantities involved, using conversion factors or unit equivalences from reliable sources, and carefully checking the dimensions on both sides of the equation to ensure they are consistent.

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