First slide

Dimensions of physical quantities

Question

A new system is formed such that it uses force, energy and velocity as fundamental quantities with units 20N, 200J and 5 ms^-1. Calculate the unit of mass ( in kg) in this new system

Moderate

Solution

$\begin{array}{l} F = 20 N, E = 200 J, v = 5 {ms}^{- 1} \\ Since E = FL \\ \Rightarrow L = \frac{E}{F} = \frac{200}{20} = 10 m \\ Since v = {LT}^{- 1} \\ \Rightarrow 5 = 10 T^{- 1} \\ \Rightarrow T = 2 s \end{array} \begin{array}{l} Further F = {MLT}^{- 2} \\ \Rightarrow 20 = M (10) (2)^{- 2} \\ \Rightarrow M = \frac{80}{10} = 8 kg \end{array}$

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