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

Question

If momentum [ P ], area [ A ] and time [ T ] are taken as fundamental quantities, then the dimensional formula for coefficient of viscosity is : (A) [ P A -1 T 0] (B) [ P A T -1] (C) [ PA -1 T ] (D) [ P A -1 T -1]

Tardigrade Admin · Accepted Answer

Viscosity = pascal.second P x A y T z =[ M 1 L -1 T -1] [ M 1 L +1 T -1] x [ L 2] y [ T 1] 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

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

$[P A^{- 1} T^{0}]$

$[P A T^{- 1}]$

$[P A^{- 1} T]$

$[P A^{- 1} T^{- 1}]$

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

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

[PA−1T0]

[PAT−1]

[PA−1T]

[PA−1T−1]