The "dimensions" of the quantities on which M depends are:--

[sigma] = (Mass)^1 (Length)^(-3),

T = (Force)^1 (Length)^(-1) = (Mass)^1 (Time)^(-2),

g = Acceleration = (Length)^1 (Time)^(-2),

of which M, a mass, is to be expressed as a function. If we assume