Which quantity among the following has neither units nor dimensions?
Which quantity among the following has neither units nor dimensions?
Relative velocity
Relative density
Angle
Energy
Solution
Relative velocity $\left(v_A \pm v_B\right)$ for two bodies $A$ and
$B$ has both units $\left(\mathrm{ms}^{-1}\right)$ and dimensions $\left[\mathrm{LT}^{-1}\right]$. Relative density of two substances $\left(\rho=\frac{\rho_A}{\rho_B}\right) A$ and B have no units and no dimensions.
Angle is measured in radian. Thus, it has units but no dimensions.
Energy is measured in joule and has dimensions
$\left[\mathrm{ML}^2 \mathrm{~T}^{-2}\right]$
Hence, only relative density has neither unit nor dimensions