Dimensional analysis problem

Question

A = K × B²

We know A is measured in Newtons and B in meters. What is the dimension of K?

Answer 1

By F = ma, we know that a Newton is a (kg)(m)/(s²)

Since A = K B², then is K = A/B² so:

K = (kg*m)/(s²)/m² = kg/(m*s²) (just to avoid confusion, that kg in the numerator and both m and s² in the denominator). You could also call it a Newton per meter squared.