A certain physical quantity is calculated from the formula $\frac{\pi}{3}\left(a^2-b^2\right) h d$, where $a…
A certain physical quantity is calculated from the formula $\frac{\pi}{3}\left(a^2-b^2\right) h d$, where $a, b$ and $h$ are all lengths and $d$ is density. The physical quantity being calculated is
velocity
volume
mass
acceleration
Solution
$\frac{\pi}{3}\left(a^2-b^2\right)$ hd ...(1)
a, b, h has length "l" so there unit is $\mathrm{m}(\mathrm{L})$ $\mathrm{d}=$ density $=\frac{\text { Mass }}{\text { volume }}=\frac{\mathrm{kg}}{\mathrm{m}^3}=\frac{\mathrm{M}}{\mathrm{L}^3}$
$\frac{\pi}{3}$ has no dimensions
from equation (1)
Now, $\left(\mathrm{L}^2-\mathrm{L}^2\right) \frac{\mathrm{M}}{\mathrm{L}^3}(\mathrm{~L})$
$\frac{\mathrm{L}^3 \mathrm{M}}{\mathrm{L}^3}=\mathrm{M} \Rightarrow$ Mass