Correct Answer - Option 1 : ML
-1T
-1
CONCEPT:
-
Viscous force (F): When a layer of fluid slips or tends to slip on adjacent layers in contact, the two layers exert tangential force on each other which tries to destroy the relative motion between them.
- The property of a fluid due to which it opposes the relative motion between its different layers is called viscosity (or fluid friction or internal friction) and the force between the layers opposing the relative motion is called viscous force.
- The force acting between the different layers of a fluid is given by
Where η = coefficient of viscosity, A = area of the plane and dv/dx = velocity gradient.
- A negative sign is employed because viscous force acts in a direction opposite to the flow of liquid.
EXPLANATION:
- The dimensional formula is defined as the expression of the physical quantity in terms of mass, length, time, and ampere.
- The above equation can be written as,
\(\Rightarrow \eta = - \frac{{F\;\left( {\frac{{dx}}{{dv}}} \right)}}{A}\)
Now,
Force = mass × acceleration
Dimensional formula of force (F) = [M] × [LT-2] = [MLT-2]
Dimensional formula of velocity (v) = [LT-1]
Dimensional formula of distance (x) = [L]
Dimensional formula of (dx/dv) = [T]
Dimensional formula of area (A) = [L2]
- The dimensional formula of viscosity (η) is
\(\Rightarrow \eta = \frac{{\left[ {{M^1}{L^1}{T^{ - 2}}} \right]\left[ T \right]\;}}{{\left[ {{L^2}} \right]}} = \left[ {M{L^{ - 1}}{T^{ - 1}}} \right]\)
- Hence, option 1 is correct.
