Dimension of Spring Force Constant

Theorem
The dimension of a spring force constant is $M T^{-2}$.

Proof
From Hooke's Law, we have:


 * $\mathbf F = -k \mathbf x$

where:
 * $\mathbf F$ is a force, of dimension $M L T^{-2}$;
 * $x$ is a displacement, of dimension $L$.

Let the dimension of $k$ be $D$.

Then we have:
 * $M L T^{-2} = D L$

from which the result follows immediately:
 * $D = M T^{-2}$