\[\begin{align} \frac{1}{2}m{{v}^{2}}=\frac{1}{2}mv_{0}^{2}+\sqrt{mgh} \\ v={{v}_{0}}+a{{t}^{2}} \\ ma={{v}^{2}} \\ \end{align}\] Do the dimensional analysis of each equation and explain why the equations cannot be correct.

(b) Is it possible for two quantities to have same units but different dimensions?

\[T=2\pi \sqrt{\frac{l}{g}}\] Where

a) $\frac{{{v}^{2}}}{xa}$

b) $\sqrt{\frac{x}{a}}$

c) $\frac{1}{2}at^2$

**Download Dimensional analysis worksheet as pdf **

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