Dimensional analysis of momentum and force expressions

[budd99]

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!

 

[Redbelly98]

Welcome to Physics Forums

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.

 

[budd99]

Welcome to Physics Forums

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?

 

[Redbelly98]

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.

 

[budd99]

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...

 

[Redbelly98]

That's correct. Yes, r has dimensions of Length, so use L for its dimension.