Question

Write down the units and dimensional formulae of following physical quantities:
$Force=mass\times acceleration$

Answer 1

Units and dimensional formula of force:

• Force can be described as a push or pull that tends to change the position, direction, or shape of an object.
• Mathematically, it can be given as $Force=mass\times acceleration$ .
• So, the unit of force$=kg\times m{s}^{-2}=kgm{s}^{-2}$, i.e., kilogram metre per second square.
• This unit in the SI system is called Newton (N).
• Write the formula of force in terms of fundamental quantities to find the dimensional formula:
  $$\begin{gathered} Force=mass\times acceleration \\ =mass\times \frac{dis\tan ce}{{\left(time\right)}^2} \\ =mass\times \frac{length}{{\left(time\right)}^2} \\ =mass\times length\times {{\left(time\right)}^{-2}}_{} \end{gathered}$$
  $\left[F\right]=\left[M\right]\times \left[L\right]\times \left[T^{-2}\right]=\left[ML{T}^{-2}\right]$

Thus, the unit of force is $Newton\left(N\right),i.e.,kgm{s}^{-2}$ , and its dimensional formula is $\left[ML{T}^{-2}\right]$.