Question

Velocity V of a streched string depends on tension T and mass per unit length M of the string. Create an equation for velocity V using dimensional analysis?

Answer 1

v = k T^a M^b

m/s = (kg m/s^2)^a (kg/m)^b

m^1/s^1 = kg^a kg^b * m^a /m^b * 1/s^2a

looks like a = .5 for s^-1 = s^-2a

b must be -a for kg^(a+b) =kg^0 = 1
so b = -.5

now m
m^1 = ?? m^.5/m^-.5 = m^(.5+.5)= m^1 yes

so
v = k T^.5 M^-.5
v = k sqrt (T/M)