Write down the units and dimensional formulae of following physical quantities:
$K E = \frac{m a s s \times {(s p e e d)}^{2}}{2}$

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Solution

Units and dimensional formula of kinetic energy:
Kinetic energy may be defined as the energy possessed by an object (or body) by virtue of its motion.
Mathematically, it can be given as $K E = \frac{m a s s \times {(s p e e d)}^{2}}{2}$ .
So, the unit of KE $= k g \times {(m s^{- 1})}^{2} = k g m^{2} s^{- 2}$ , i.e., kilogram metre square per second square.
This unit in SI system is called Joule $(J)$ , which in simpler terms is nothing but Newton-metre $(N - m)$ .
Dimensional formula of KE:
$K E = \frac{m a s s \times {(s p e e d)}^{2}}{2} [K E] = [M] \times {[L T^{- 1}]}^{2} = [M L^{2} T^{- 2}]$
Thus, the unit of KE is $J o u l e (J), i . e ., N - m o r k g m^{2} s^{- 2}$ and its dimensional formula is $[M L^{2} T^{- 2}]$ .

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