A student writes an equation $\frac{1}{2} m v^2 = mgh$. What are the dimensions of the right-hand si

Question

A student writes an equation $\frac{1}{2} m v^2 = mgh$. What are the dimensions of the right-hand side of this equation?

Professor PC Thomas Classes · Answer

The dimensions of the right-hand side ($mgh$) are $[M] 	imes [L T^{-2}] 	imes [L] = [M L^2 T^{-2}]$. This perfectly matches the dimensions of kinetic energy on the left side.