First slide

Dimensions of physical quantities

Question

Consider a new system of units in which the unit of mass is $α$ kg, unit of length is $β$ m and that of time is $γ$ s. The value of calorie in the new system is calculated to be $4.18 α^{- x} β^{- y} γ^{z}$ . Find the values of z.

Moderate

Solution

$\begin{array}{l} n_{2} = n_{1} {(\frac{M_{1}}{M_{2}})}^{1} {(\frac{L_{1}}{L_{2}})}^{2} {(\frac{T_{1}}{T_{2}})}^{- 2} \\ \Rightarrow n_{2} = 4 .18 (\frac{1 kg}{αkg}) {(\frac{1 m}{βm})}^{2} {(\frac{1 s}{γs})}^{- 2} \\ \Rightarrow n_{2} = 4 .18 α^{- 1} β^{- 2} γ^{2} \\ So, 4 .18 J = 4 .18 α^{- 1} β^{- 2} γ^{2} new units \end{array}$

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