A) \[[M{{L}^{-1}}{{T}^{-1}}\text{ }\!\!]\!\!\text{ }\]
B) \[[M{{L}^{-1}}{{T}^{-3}}\text{ }\!\!]\!\!\text{ }\]
C) \[[M{{L}^{-2}}{{T}^{-2}}\text{ }\!\!]\!\!\text{ }\]
D) \[[M{{L}^{2}}{{T}^{-2}}\text{ }\!\!]\!\!\text{ }\]
Correct Answer: A
Solution :
Coefficient of viscosity of a liquid is defined as the viscous force (F) per unit area [a] of contact between two layers having a unit Velocity gradient between them. \[\therefore \] \[\eta =\frac{F}{A\,\,(\Delta v/\Delta z)}\] \[\therefore \] Dimensions of \[\eta =\frac{[ML{{T}^{-2}}]}{[{{L}^{2}}][L{{T}^{-1}}/L]}=\frac{[ML{{T}^{-2}}]}{[{{L}^{2}}{{T}^{-1}}]}=[M{{L}^{-1}}{{T}^{-1}}]\] Alternative: The SI unit of coefficient of viscosity is \[kg{{m}^{-1}}{{s}^{-1}}\], hence dimensions are\[[M{{L}^{-1}}{{T}^{-1}}]\].
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