If the dimensions of a physical quantity are given by $\mathrm{M}^{\mathrm{a}} \mathrm{L}^{\mathrm{b}}…
If the dimensions of a physical quantity are given by $\mathrm{M}^{\mathrm{a}} \mathrm{L}^{\mathrm{b}} \mathrm{T}^c$, then the physical quantity will be
pressure if $\mathrm{a}=1, \mathrm{~b}=-1, \mathrm{c}=-2$
velocity if $a=1, b=0, c=-1$
acceleration if a $=1, b=1, c=-2$
force if $\mathrm{a}=0, \mathrm{~b}=-1, \mathrm{c}=-2$
Solution
(i) Dimensions of velocity $=\left[\mathrm{M}^0 \mathrm{~L}^1 \mathrm{~T}^{-1}\right]$ Here, $a=0, b=1, c=-1$
(ii) Dimensions of acceleration $=\left[\mathrm{M}^0 \mathrm{~L}^1 \mathrm{~T}^{-2}\right]$
Here, $\quad a=0, b=1, c=-2$
(iii) Dimensions of force $=\left[\mathrm{M}^1 \mathrm{~L}^1 \mathrm{~T}^{-2}\right]$
Here, $a=1, b=1, T=-2$
(iv) Dimensions of pressure $=\left[\mathrm{M}^1 \mathrm{~L}^{-1} \mathrm{~T}^{-2}\right]$
$\therefore$ Here, $\quad \mathrm{a}=1, \mathrm{~b}=-1, \mathrm{c}=-2$
$\therefore$ The physical quantity is pressure.