Question

The SI unit of coefficient of viscosity is
$\begin{align}
  & \text{A}\text{. N-}{{\text{m}}^{2}} \\
 & \text{B}\text{. N-s} \\
 & \text{C}\text{. N-s/}{{\text{m}}^{2}} \\
 & \text{D}\text{. N-}{{\text{m}}^{2}}/s \\
\end{align}$

Answer 1

Hint: Study about the unit systems used for measurements. Learn the quantities used in the SI unit system. Define coefficient of viscosity and obtain the mathematical expression for the coefficient of viscosity. Now, find the SI unit of the constituent quantities and using them we can find our answer.

Complete step by step answer:
The SI units or the International System of Units is a system of physical units based on the meter, kilogram, second, ampere, kelvin, candela and mole. We use a set of prefixes to express the multiplication or division by power of 10.
Viscosity of a fluid can be defined as the resistance of the liquid. The coefficient of viscosity can be defined as the viscous force acting per unit area between two adjacent layers of fluid where the velocity gradient is normal to the flow of the fluid.
We can express the viscous force as,
$f=\eta A\dfrac{dv}{dx}$
Where, $\eta $ is the coefficient of viscosity, A is the area and $\dfrac{dv}{dx}$ is the velocity gradient.
So, we can write that,
$\eta =\dfrac{f}{A\dfrac{dv}{dx}}$
Now, the SI unit of force is Newton or N.
Again, the SI unit of area is ${{m}^{2}}$ and the SI unit of velocity gradient is ${{s}^{-1}}$ .
So, we can write that the SI unit of coefficient of viscosity is,
$\eta =\dfrac{N}{{{m}^{2}}{{s}^{-1}}}=N-s/{{m}^{2}}$
The correct option is (C).

Note: Coefficient viscosity gives us the viscous force on an object moving in water. The larger is the coefficient of viscosity of a fluid, the larger will be the viscous force or opposing force on objects moving in that fluid.