Write down the units and dimensional formulae of following physical quantities:
$M o m e n t u m = m a s s \times v e l o c i t y$

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Solution

Units and dimensional formula of momentum:
Momentum can be described as the product of mass and velocity of an object.
Mathematically, it can be given as $M o m e n t u m = m a s s \times v e l o c i t y$ .
So, the unit of momentum $= M a s s \times \frac{D i s \tan c e}{T I m e} = k g m s^{- 1}$ , i.e., kilogram metres per second.
Write the formula of momentum in terms of fundamental quantities to find the dimensional formula:
$M o m e n t u m = m a s s \times \frac{d i s \tan c e}{t i m e} = m a s s \times \frac{l e n g t h}{t i m e} = (m a s s) \times (l e n g t h) \times {(t i m e)}^{- 1} [M o m e n t u m] = [M] [L] [T^{- 1}] = [M L T^{- 1}]$
Thus, the unit of momentum is $k g m s^{- 1}$ and its dimensional formula is $[M L T^{- 1}]$ .

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