# In what cases does dimensional analysis fail?

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berkeman
Mentor
The dimensiona of lambda is (time)^-1, time inverse, basically frequency. .M is mass. That is given. I dont or I am not quite sure on c
The starting equation contains forces. What are the units of force in mks? Each term has to have those same units, right? That helps you figure out the units for the other terms that introduced in the later equations. And yes, since λt is in the exponent, and since the exponent needs to be dimensionless, the units of λ need to be 1/s.

A.T.
Science Advisor
In what cases does dimensional analysis fails?
Not sure what 'fails' means here, but dimensional homogeneity doesn't guarantee that your equation is physically sensible:

https://en.wikipedia.org/wiki/Dimensional_analysis#Dimensional_homogeneity
Even when two physical quantities have identical dimensions, it may nevertheless be meaningless to compare or add them. For example, although torque and energy share the dimension L2MT−2, they are fundamentally different physical quantities.

berkeman
The starting equation contains forces. What are the units of force in mks? Each term has to have those same units, right? That helps you figure out the units for the other terms that introduced in the later equations. And yes, since λt is in the exponent, and since the exponent needs to be dimensionless, the units of λ need to be 1/s.
Yeah ok so c has units of M(T)^-1

Not sure what 'fails' means here, but dimensional homogeneity doesn't guarantee that your equation is physically sensible:

https://en.wikipedia.org/wiki/Dimensional_analysis#Dimensional_homogeneity
Even when two physical quantities have identical dimensions, it may nevertheless be meaningless to compare or add them. For example, although torque and energy share the dimension L2MT−2, they are fundamentally different physical quantities.
Yeah sorry. I think I did'nt frame my question in the proper way. So the math part of the equation can be checked out but it will not be wise to try and infer the physics aspect of it

Chestermiller
Mentor
The dimensiona of lambda is (time)^-1, time inverse, basically frequency. .M is mass. That is given. I dont or I am not quite sure on c
That’s correct.