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Units and Measurements — Physics STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 SciencePhysicsUnits and Measurements3 Marks
Question
E, m, I and G denote energy, mass, angular momentum and gravitational constant respectively. Determine the dimensions of $\frac{\text{El}^2}{\text{m}^5\text{G}^2}$
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Answer

Dimensions of $\text{E}=[\text{M}\text{L}^2\text{T}^{-2}]$ Dimensions of $\text{l}=[\text{ML}^2\text{T}^{-2}]$ Dimensions of $\text{m}​=[\text{M}]​$ Dimensions of $\text{G}=[\text{M}^{-1}\text{L}^{3}\text{T}^{-2}]$ $\therefore$ Dimensions of $\frac{\text{El}^2}{\text{m}^5\text{G}^2}$ $=\frac{[\text{ML}^2\text{T}^{-2}​​]{[\text{ML}^2\text{T}^{-2}]^2}}{[\text{M}]^5[\text{M}^{-1}\text{L}^{3}\text{T}^{2}]^{-2}}=1$ Thus $\frac{\text{El}^2}{\text{m}^5\text{G}^2}$is dimensionless.

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