Considering the Principle of Homogeneity of Dimensions, is the following equation correct? F=mh, where F = force , and h = height.

The Principle of Homogeneity of Dimensions states that all terms inside a physical formula must be the same. Really, it is a bad idea to add meters to kilograms (multiplying meters by kilograms is okay).

There are only two terms in our formula `F = m*h,` `F` and `m*h.` We have to check and compare their dimensions.

Force `F` has the dimension of Newtons (`N`). `N` is the same as `kg*m/s^2`; we can derive this from Newton's Second Law `F = ma.` Height `h` has the dimension of meters (`m`), and mass `m` has the dimension of `kg.` In terms of dimensional formulas `F = [M*L*T^(-2)],` `m = [M]` and `h = [L].`

So there is `[M*L*T^(-2)]` at the left and `[M*L]` at the right. These dimensions are different, so no, this formula cannot be correct.