Question

Write down the units and dimensional formulae of following physical quantities:
$PE=mgh$

Answer 1

Units and dimensional formula of potential energy:

• Potential energy is the form of energy that is stored inside a body due to its position.
• Mathematically, it can be given as $PE=mgh$.
• So, the unit of PE $=kg\times m{s}^{-2}\times m=kg{m}^2{s}^{-2}$, i.e., kilogram metre square per second square.
• This unit in SI system is called Joule $\left(J\right)$, which in simpler terms is nothing but Newton-metre $(N-m)$.
• Write the formula of potential energy in terms of fundamental quantities to find the dimensional formula:
  $$\begin{gathered} PE=mass\times accelerationduetogravity\times height \\ =mass\times \frac{velocity}{time}\times length \\ =mass\times \frac{length}{{\left(time\right)}^2}\times length \\ =mass\times {\left(length\right)}^2\times {\left(time\right)}^{-2} \\ \left[PE\right]=\left[M\right]\times \left[L^2\right]\times \left[T^{-2}\right]=\left[M{L}^2{T}^{-2}\right] \end{gathered}$$

Thus, the unit of potential energy is $Joule\left(J\right),i.e.,N-morkg{m}^2{s}^{-2}$ and its dimensional formula is $\left[M{L}^2{T}^{-2}\right]$.