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1.Units, Dimensions and Measurement
medium
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 constant called coefficient of viscosity. The dimension of $\eta $ are
A
$[M{L^2}{T^{ - 2}}]$
B
$[M{L^{ - 1}}{T^{ - 1}}]$
C
$[M{L^{ - 2}}{T^{ - 2}}]$
D
$[{M^0}{L^0}{T^0}]$
(AIPMT-1990)
Solution
(b) $F = – \eta A\frac{{\Delta v}}{{\Delta z}} \Rightarrow [\eta ] = [M{L^{ – 1}}{T^{ – 1}}]$
As $F = [ML{T^{ – 2}}],\,\,A = [{L^2}],\,\frac{{\Delta v}}{{\Delta z}} = [{T^{ – 1}}]$
Standard 11
Physics
