According to Newton,the viscous force acting | vedclass

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Question

(B) The formula for viscous force is $F = - \eta A \frac{\Delta v}{\Delta z}$.Rearranging for $\eta$,we get $\eta = \frac{F}{A (\Delta v / \Delta z)}$

Vedclass · Accepted Answer

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

Vedclass · Answer

(B) The formula for viscous force is $F = - \eta A \frac{\Delta v}{\Delta z}$.Rearranging for $\eta$,we get $\eta = \frac{F}{A (\Delta v / \Delta z)}$.Substituting the dimensions of each quantity:Force $F = [M L T^{-2}]$Area $A = [L^2]$Velocity gradient $\frac{\Delta v}{\Delta z} = \frac{[L T^{-1}]}{[L]} = [T^{-1}]$Now,calculating the dimensions of $\eta$:$[\eta] = \frac{[M L T^{-2}]}{[L^2] [T^{-1}]} = [M L^{1-2} T^{-2+1}] = [M L^{-1} T^{-1}]$.Thus,the correct option is $B$.

Column-$1$	Column-$2$
$(a)$ Wave vector	$(i)$ $M^1L^0T^{-3}$
$(b)$ Linear mass density	$(ii)$ $M^1L^{-1}T^{-2}$
$(c)$ Intensity of a wave	$(iii)$ $M^0L^{-1}T^0$
$(d)$ Volume elasticity coefficient	$(iv)$ $M^1L^{-1}T^0$

According to Newton,the viscous force acting between liquid layers of area $A$ and velocity gradient $\Delta v/\Delta z$ is given by $F = - \eta A \frac{\Delta v}{\Delta z}$,where $\eta$ is a constant called the coefficient of viscosity. The dimensions of $\eta$ are:

Similar Questions

Match Column-$1$ with Column-$2$.
Column-$1$ Column-$2$
$(a)$ Wave vector $(i)$ $M^1L^0T^{-3}$
$(b)$ Linear mass density $(ii)$ $M^1L^{-1}T^{-2}$
$(c)$ Intensity of a wave $(iii)$ $M^0L^{-1}T^0$
$(d)$ Volume elasticity coefficient $(iv)$ $M^1L^{-1}T^0$

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