$($I need step by step solution only with proper explanation and solving of each and every step $)$ The following four equations are asserted to be fundamental equations of physical systems:

i$.F=A(\frac{N^{5}T}{V^3}{)}^{\frac{1}{2}}$

ii$.G=B{T}^{\frac{1}{2}}{P}^{2}N$

iii. $H=(\frac{C{S}^2{P}^{\frac{1}{2}}}{N})$

iv$.U=D(\frac{S^3{V}^4}{N^5}{)}^{\frac{1}{2}}$

Among the aforementioned equations, which of these violate the criteria of stability? Assume

$A,B,C$ and D to be positive constants.