Write down the units and dimensional formulae of following physical quantities:
$E l a s t i c P E = \frac{S p r i n g C o n s \tan t \times {(e l o n g a t i o n)}^{2}}{2}$

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Solution

Units and dimensional formula of elastic potential energy:
Elastic potential energy is defined as the potential energy that is stored inside a spring due to an external action like stretching or compression.
Mathematically, it can be given as $E l a s t i c P E = \frac{S p r i n g C o n s \tan t \times {(e l o n g a t i o n)}^{2}}{2}$ .
So, the SI unit of elastic PE $= N m^{- 1} \times m^{2} = N m$ , i.e., Newton meter is nothing but Joule $(J)$ .
Use its unit to find the dimensional formula of elastic PE:
$E l a s t i c P E = N \times m [E l a s t i c P E] = [M L T^{- 2}] \times [L] = [M L^{2} T^{- 2}]$
Thus, the unit of elastic PE is $J o u l e (J), i . e ., N e w t o n m e t r e, i . e ., N - m$ and its dimensional formula is $[M L^{2} T^{- 2}]$ .

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