Physics - Unit & Dimension Question with Solution | TestHub

As joule is the SI unit of energy and dimensional formula for energy is $\left[{\mathrm{ML}}^2{\mathrm{T}}^{-2}\right]$. In this question, we have to convert one unit into another, therefore $\begin{array}{rl}{\eta }_1\left[M_1{L}_1^2{T}_1^{-2}\right]& ={\eta }_2\left[M_2{L}_2^2{T}_2^{-2}\right]\\ \Rightarrow {\eta }_2& ={\eta }_1{\left[\frac{M_1}{M_2}\right]}^1{\left[\frac{L_1}{L_2}\right]}^2{\left[\frac{T_1}{T_2}\right]}^{-2}\\ & =1\times {\left[\frac{1\mathrm{kg}}{10\mathrm{kg}}\right]}^1{\left[\frac{1\mathrm{m}}{1\mathrm{km}}\right]}^2{\left[\frac{1\mathrm{s}}{1\min }\right]}^{-2}\\ & =1\times {\left[\frac{1\mathrm{kg}}{10\mathrm{kg}}\right]}^1{\left[\frac{1\mathrm{m}}{10^3\mathrm{m}}\right]}^2{\left[\frac{1\mathrm{s}}{60\mathrm{s}}\right]}^{-2}\\ & =1\times 10^{-1}\times 10^{-6}\times 36\times 10^2\\ {\eta }_2& =36\times 10^{-5}\mathrm{J}\end{array}$