Question:
Test if the following are dimensionally correct:
(a) $h=\frac{25 \cos \theta}{\rho r g}$
(b) $v=\sqrt{\frac{p}{\rho}}$
(c) $\frac{\pi P t r^{4}}{8 n l}$
(D) $\frac{1}{2 \pi} \sqrt{\frac{m g l}{I}}$
Solution:
(a) $h=\frac{25 \cos \theta}{\rho r g}$
Here, $h=[\mathrm{L}], \mathrm{S}=\mathrm{F} / \mathrm{L}=\left[\mathrm{MT}^{-2}\right], \rho=\left[\mathrm{ML}^{-3}\right], \mathrm{r}=[\mathrm{L}], \mathrm{g}=\left[\mathrm{LT}^{-2}\right]$
So, $\frac{2 \sec \theta}{p r g}$ $=\left[\mathrm{MT}^{-2}\right] / /\left[\mathrm{ML}^{-3} \mathrm{~L}^{2} \mathrm{~T}^{-2}\right]=[\mathrm{L}]$
This relation is correct
