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1.Units, Dimensions and Measurement
medium
If momentum $[ P ]$, area $[ A ]$ and time $[ T ]$ are taken as fundamental quantities, then the dimensional formula for coefficient of viscosity is :
A
$\left[ PA ^{-1} T ^{0}\right]$
B
$\left[ PA T ^{-1}\right]$
C
$\left[ PA ^{-1} T \right]$
D
$\left[ PA ^{-1} T ^{-1}\right]$
(JEE MAIN-2022)
Solution
Viscosity $=$ pascal.second
$P ^{ x } A ^{ y } T ^{z}=\left[ M ^{1} L ^{-1} T ^{-1}\right]$
$\left[ M ^{1} L ^{+1} T ^{-1}\right]^{ x }\left[ L ^{2}\right]^{y}\left[ T ^{1}\right]^{z}= M ^{1} L ^{-1} T ^{-1}$
$M ^{ x } L ^{+ x +2 y } T ^{- x + z }= M ^{1} L ^{-1} T ^{-1}$
$x=1 \quad x+2 y=-1 \quad-x+z=-1$
$y=-1$
$z=0$
Viscosity $= P ^{1} A ^{-1} T ^{0}$
Standard 11
Physics
