Question

what are dimensional formulas of linear density ,retardation,areal velocity,tension in string and number density?

Answer 1

Linear density=Mass/length=[M]/[L]
$\left[{\mathrm{M}}^1{\mathrm{L}}^{-1}{\mathrm{T}}^0\right]$
Retardation=Negative acceleration=Change in velocity/time
$\frac{[\mathrm{L}/\mathrm{T}]}{\left[\mathrm{T}\right]}={\mathrm{LT}}^{-2}=\left[{\mathrm{M}}^0{\mathrm{L}}^1{\mathrm{T}}^{-2}\right]$

Areal velocity=Area / time

$\frac{\left[{\mathrm{L}}^2\right]}{\left[\mathrm{T}\right]}=\left[{\mathrm{M}}^0{\mathrm{L}}^2{\mathrm{T}}^{-1}\right]$
Tension=Force
$$\begin{gathered} \mathrm{F}=\mathrm{ma}=\left[\mathrm{M}\right]\left[{\mathrm{LT}}^{-2}\right] \\ =\left[{\mathrm{M}}^1{\mathrm{L}}^1{\mathrm{T}}^{-2}\right] \end{gathered}$$
Number density is number of particles per unit volume.
Thus,
$\left[{\mathrm{M}}^0{\mathrm{L}}^{-3}{\mathrm{T}}^0\right]$