If the dimensions of a physical quantity are given by $\left[\mathrm{M}^{\mathrm{a}} \mathrm{L}^{\mathrm{b}}…
If the dimensions of a physical quantity are given by $\left[\mathrm{M}^{\mathrm{a}} \mathrm{L}^{\mathrm{b}} \mathrm{T}^{c}\right]$ then the physical
quantity is
velocity if $a=-1, b=0, c=+1$
force if $a=-1, b=1, c=-2$
pressure if $a = 1,~ b = −1,~ c = 2$
acceleration if $\mathrm{a}=1, \mathrm{~b}=1, \mathrm{c}=-2$
Solution
A. pressure if $a=1, b=-1, c=2$
Dimensions of velocity $=\left[\mathrm{M}^{0} \mathrm{~L}^{1} \mathrm{~T}^{-1}\right]$
Here, $a=0, b=1, c=-1$
Dimension of acceleration $=\left[\mathrm{M}^{0} \mathrm{~L}^{1} \mathrm{~T}^{-2}\right]$
Dimension of force $=\left[\mathrm{M}^{1} \mathrm{~L}^{1} \mathrm{~T}^{-2}\right]$
Dimension of pressure $=\left[\mathrm{M}^{1} \mathrm{~L}^{-1} \mathrm{~T}^{-2}\right.$
The physical quantity is pressure.