Question

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

Answer 1

From the principle of homogeneity,

Dimension of ${\beta }^3=$ Dimension of Density $=\left[M{L}^{-3}\right]$

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

Now, Dimension of Force = (Dimension of $\alpha$)/(Dimension of Density)

$\Rightarrow \left[ML{T}^{-2}\right]=\frac{Dimensionof\alpha }{\left[M{L}^{-3}\right]}$

$\Rightarrow Dimensionof\alpha =\left[M^2{L}^{-2}{T}^{-2}\right]$