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Q.

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

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a

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

b

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

c

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

d

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

answer is A.

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Detailed Solution

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Viscosity = pascal. second

$\begin{array}{l} P^{x} A^{y} T^{z} = [M^{1} L^{- 1} T^{- 1}] \\ {[M^{1} L^{+ 1} T^{- 1}]}^{x} {[L^{2}]}^{y} {[T^{1}]}^{z} = M^{1} L^{- 1} T^{- 1} \\ M^{x} L^{+ x + 2 y} T^{- x + z} = M^{1} L^{- 1} T^{- 1} \\ x = 1 x + 2 y = - 1 - x + z = - 1 \\ y = - 1 \\ z = 0 \end{array}$

Viscosity $= P A^{- 1} T^{0}$

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