Question

Write down the units and dimensional formulae of following physical quantities:

$Torque=force\times length$

Answer 1

Units and dimensional formula of torque:

• Torque: It can be defined as the turning effect of a force.
• Mathematically, it can be given as $Torque=force\times length$.
• So, the SI unit of torque $=N\times m=Nm$, i.e., Newton metre.
• Use its unit to find the dimensional formula of elastic PE:
  $$\begin{gathered} Torque=force\times length \\ \left[Torque\right]=\left[ML{T}^{-2}\right]\times \left[L\right] \\ =\left[M{L}^2{T}^{-2}\right] \end{gathered}$$

Thus, the unit of torque is $Newtonmetre,i.e.,N-m$ and its dimensional formula is $\left[M{L}^2{T}^{-2}\right]$.