According to Newton, the viscous force acting between liquid layers of area A and velocity gradient Δ v/ Δ Z is given by F=-η A(Δ v/Δ Z) , where η is constant called coefficient of viscosity. The dimensional formula of η is

Question

According to Newton, the viscous force acting between liquid layers of area A and velocity gradient Δ v/ Δ Z is given by F=-η A(Δ v/Δ Z) , where η is constant called coefficient of viscosity. The dimensional formula of η is (A) [ML-2T-2] (B) [M0L0T0] (C) [ML2T-2] (D) [ML-1T-1]

Tardigrade Admin · Accepted Answer

Dimensions of force F=[MLT-2] Dimensions of velocity gradient (Δ v/Δ Z)=([LT-1]/[L]) =[T-1] Dimensions of area A=[L2] Given F=-η A(Δ v/Δ Z) Dimensional formula for coefficient of viscocity η=(F/(A) big((Δ v)Δ Z big))=([MLT-2]/[L2][T-1])=[ML-1T-1]

Q. According to Newton, the viscous force acting between liquid layers of area $A$ and velocity gradient $Δ v /Δ Z$ is given by $F = - η A \frac{Δ v}{Δ Z}$ , where $η$ is constant called coefficient of viscosity. The dimensional formula of $η$ is

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

$[M^{0} L^{0} T^{0}]$

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

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

Q. According to Newton, the viscous force acting between liquid layers of area A and velocity gradient Δv/ΔZ is given by F=−ηAΔZΔv​ , where η is constant called coefficient of viscosity. The dimensional formula of η is

[ML−2T−2]

[M0L0T0]

[ML2T−2]

[ML−1T−1]

Dimensions of force F=[MLT−2] Dimensions of velocity gradient ΔZΔv​=[L][LT−1]​ =[T−1] Dimensions of area A=[L2] Given F=−ηAΔZΔv​ Dimensional formula for coefficient of viscocity η=(A)(ΔZΔv​)F​=[L2][T−1][MLT−2]​=[ML−1T−1]

Q. According to Newton, the viscous force acting between liquid layers of area $A$ and velocity gradient $Δ v /Δ Z$ is given by $F = - η A \frac{Δ v}{Δ Z}$ , where $η$ is constant called coefficient of viscosity. The dimensional formula of $η$ is

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

$[M^{0} L^{0} T^{0}]$

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

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