Question

Write down the units and dimensional formulae of following physical quantities:
$Power=\frac{work}{time}$

Answer 1

Units and dimensional formula of power:

• Power can be defined as the rate at which a work is done.
• Mathematically, it can be given as $Power=\frac{work}{time}$.
• So, the unit of power $=\frac{kg{m}^2{s}^{-2}}{s}=kg{m}^2{s}^{-3}$, i.e., kilogram meter square per second cube.
• This unit in the SI system is called Watt $\left(W\right)$, which in simpler terms is nothing but Newton-metre per second $(N-m{s}^{-1})$.
• Write the formula of power in terms of fundamental quantities to find the dimensional formula:
  $$\begin{gathered} Power=\frac{work}{time}=work\times {\left(time\right)}^{-1} \\ \left[P\right]=\left[M{L}^2{T}^{-2}\right]\times \left[T^{-1}\right] \\ =\left[M{L}^2{T}^{-3}\right] \end{gathered}$$

Thus, the unit of power is $Watt\left(W\right),i.e.,N-m{s}^{-1}orkg{m}^2{s}^{-3}$ and its dimensional formula is $\left[M{L}^2{T}^{-3}\right]$.