Question

A geometry textbook gives the equation of a parabola as y = x 2, where x
and y are measured in inches. How can this equation be dimensionally correct?

Answer 1

To make the equation $y=x^2$ dimensionally correct, there must be a constant of either side with a dimension that balances both sides. Let the constant be k.

Therefore,

$y=kx^2\\ Dimensionally,\\ L=kL^2\\ k=L^{1-2}=L^{-1}$