Which one of the following represents the correct dimensions of the quantity x-where - coefficient of viscosity and - the density of a liquid-

The correct option is D [ M^0L^2T^ 1 ] Dimension of coefficient of viscocity μ= [ M L^ 1T^ 1 ] amp; dimension of density ρ = [ M L^ 3 ] #1 ...

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Byju's Answer

Standard XII

Physics

Coefficient of Viscosity

Which one of ...

Question

Which one of the following represents the correct dimensions of the quantity $x = \frac{η}{ρ}$ ,where $η =$ coefficient of viscosity and $ρ =$ the density of a liquid?

[M L^{- 2} T^{- 1}]

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[M L^{- 4} T^{- 2}]

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[M L^{- 5} T^{- 2}]

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[M^{0} L^{2} T^{- 1}]

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Solution

The correct option is D $[M^{0} L^{2} T^{- 1}]$
Dimension of coefficient of viscocity $μ = [M L^{- 1} T^{- 1}]$
& dimension of density $ρ = [M L^{- 3}]$
so the dimension of quantity $(x = \frac{η}{ρ})$ = $\frac{[M L^{- 1} T^{- 1}]}{[M L^{- 3}]} = [M^{0} L^{2} T^{- 1}]$

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Which one of the following represents the correct dimensions of the quantity x=ηρ,where η= coefficient of viscosity and ρ= the density of a liquid?

The correct option is D [M0L2T−1]Dimension of coefficient of viscocity μ=[ML−1T−1]& dimension of density ρ=[ML−3] so the dimension of quantity (x=ηρ) =[ML−1T−1][ML−3]=[M0L2T−1]

Which one of the following represents the correct dimensions of the quantity $x = \frac{η}{ρ}$ ,where $η =$ coefficient of viscosity and $ρ =$ the density of a liquid?

The correct option is D $[M^{0} L^{2} T^{- 1}]$
Dimension of coefficient of viscocity $μ = [M L^{- 1} T^{- 1}]$
& dimension of density $ρ = [M L^{- 3}]$
so the dimension of quantity $(x = \frac{η}{ρ})$ = $\frac{[M L^{- 1} T^{- 1}]}{[M L^{- 3}]} = [M^{0} L^{2} T^{- 1}]$