Explain with the help of an example why homogeneity of a physical equation is not a sufficient condition for the correctness of the equation.

1) a) Explain with the help of an example why homogeneity of a physical equation is not a sufficient condition for the correctness of the equation.
Homogeneity of a physical equation means that the units of the physical quantities on both sides of the equation are identical. While a correct equation must be dimensionally homogeneous, homogeneity alone does not guarantee correctness. This is because it does not account for dimensionless constants or numerical factors. For example, the kinetic energy of an object is $E_k = \frac{1}{2}mv^2$. If one were to write $E_k = mv^2$, the equation would still be dimensionally homogeneous (both sides have units of $\text{kg m}^2 \text{s}^{-2}$),