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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