Question

If the dimensions of a physical quantity are given by $\left[L^a{M}^b{T}^c\right]$, then the physical quantity will be

• A. force, if $a=-1,b=0,c=-2$
• B. pressure, if $a=-1,b=1,c=-2$
• C. velocity, if $a=1,b=0,c=1$
• D. acceleration, if $a=1,b=1,c=-2$

Answer 1

The correct option is B pressure, if $a=-1,b=1,c=-2$

Dimensions of force $=\left[L^1{M}^1{T}^{-2}\right]$

$\text{Pressure}=\frac{\text{Force}}{\text{Area}}$

$\therefore$ Dimensions of pressure $=\left[L^{-1}{M}^1{T}^{-2}\right]$

Dimesions of velocity $=\left[L^1{M}^0{T}^{-1}\right]$

Dimesions of acceleration $=\left[L^1{M}^0{T}^{-2}\right]$

Only option (b) is correct