Let the relation be:
Frequency v = KLafbmc
where k is a dimensionless constant
The dimension of each quantity are:
L=[M0L1To]
f=[M1L1T−2]
m=[M1L−1T0]
v=[M0L0T−1]
Thus now equating the dimension on both side of the equation:
[M0L0T−1]=[M0L1To]a[M1L1T−2]b[M1L−1T0]cthus, b = 1/2
c = −1/2
a = −1
Thus, the formula for frequency is:
V = k/L √f/m
Tags:
Physics