Dimensions related to Planck's constant H

[ODBS]

Consider a system where the three fundamentally important quantities are the speed of light C with dimensions (L)/(T), Planck's constant H with dimensions (M)(L)^2/(T), and the mass of the proton M sub p with dimension (M).
a) What combination of ratios and/or products of C, H, and M sub p will yield a new quantity of dimensions (L)?
b) What combination of ratios and/or products of C, H, and M sub p will yield a new quantity of dimensions (T)?


I have no idea how to figure this out. I am brand new to physics so any help would be greatly appreciated. Could you please solve the question and walk me through how you found the answer? I am a very literal learner and I need to see the answer along with how you found it.




This is what I came up with, not sure if it's correct:

(C^a)*(H^b)*(M^c)

L^(a+2b)=L----> a+2b=1
M^(b+c)= 1-----> b+c=0
T^(a-b)=1---->a-b=0

a=-b
b=1
a=-1
c=-1

(C^-1)*(H^1)*(M^-1)=H/C*M

-a-b=1
a+2b=0
b+c=0
b=1
a=-2
c=-1

So, H/M*c*c


part A= H/M*C
part B= H/M*C*C

 

[NihalSh]

yes, you are correct...I checked it myself. Cheers

 

[ODBS]

Thank you! I've asked another question about fcc fraction packing for a pyramidal structure. Can you take a look at it and help me out? I'm really lost on that one.

 

[ODBS]

https://www.physicsforums.com/showthread.php?t=715654

 

[NihalSh]

Thank you! I've asked another question about fcc fraction packing for a pyramidal structure. Can you take a look at it and help me out? I'm really lost on that one.

I would've if I myself had any clue! I am a student myself, I am not proficient with that topic!...I am sure others will help out!