Physics

If Force$=\dfrac{\alpha}{\beta^{3}+density}$, then find dimension of $\alpha$ and $\beta$.

SOLUTION
From the principle of homogeneity,
Dimension of $\beta^3 =$ Dimension of Density $= [ML^{-3}]$

$\Rightarrow$ Dimension of $\beta = [M^{1/3}L]$

Now, Dimension of Force = (Dimension of $\alpha$)/(Dimension of Density)
$\Rightarrow [MLT^{-2}] = \dfrac{Dimension \; of \; \alpha}{[ML^{-3}]}$

$\Rightarrow Dimension \; of \; \alpha = [M^2L^{-2}T^{-2}]$

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Subjective Medium Published on 18th 08, 2020
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