Question

The dimensional consistency of the terms can be used to detect algebraic errors. Consider the following equation:FA=gA+ρv2+maL2where v is a velocity's magnitude, a is an acceleration's magnitude, A is an area, m is a mass, L is a length (or distance), g is another acceleration's magnitude, ρ is a density (mass per unit volume), and F
is a force's magnitude. Which terms are dimensionally homogeneous?
Check all that apply. I know the answers are1 2 and 4 but don't know why. explain so I can understand.
1) ρv^2
2) ma/L^2
3) g/A
4) F/A

Answer 1

equation: F/A = g/A+ ρv^2 + ma/L^2

Answer 2

F/ A = g / A + ρ v^2 +m a / L^2

F/A = Newtons/ m^2 = kg m/s^2 / m^2 = kg / m s^2
m a/L^2 = kg m/s^2 / m^2 = kg / m s^2 same
g / A = m/s^2 / m^2 = 1 / m s^2 NO KILOGRAMS !
ρ v^2 = kg/m^3 * m^2/s^2 = kg / m s^2 same