Consider a system where the three fundamentally important quantities are the spe
ID: 2140260 • Letter: C
Question
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)?
Please show me how to find the answer and provide the correct answer. The person to do both will get the points.
Explanation / Answer
(C^a)x(H^b)(M^c)
for a part -
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)x(H^1)x(M^-1 ) = H/(C*M)
simillarely for part (b)
-a-b=1
a+2b=0
b+c=0
b=1
a=-2
c=-1
H/(M*C*C)
a) H/(M*C)
b)H/(M*C*C)