Question

If momentum $[ P ]$, area $[ A ]$ and time $[ T ]$ are taken as fundamental quantities, then the dimensional formula for coefficient of viscosity is :

• A. $\left[ P A ^{-1} T ^0\right]$
• B. $\left[ P A T ^{-1}\right]$
• C. $\left[ PA ^{-1} T \right]$
• D. $\left[ P A ^{-1} T ^{-1}\right]$

Answer 1

Answer: (A)

Viscosity $=$ pascal.second
$ P ^{ x } A ^{ y } T ^{ z }=\left[ M ^1 L ^{-1} T ^{-1}\right] $
$ {\left[ M ^1 L ^{+1} T ^{-1}\right]^{ x }\left[ L ^2\right]^{ y }\left[ T ^1\right]^{ z }= M ^1 L ^{-1} T ^{-1}} $
$ M ^{ x } L ^{+ x +2 y } T ^{- x + z }= M ^1 L ^{-1} T ^{-1} $
$ x =1 \,\, x +2 y =-1 \,\,- x + z =-1 $
$ y =-1 $
$ z =0$
Viscosity $= P ^1 A ^{-1} T ^0$