# What is the SI unit of viscosity coefficient($\eta$)?

A- Pascal

B- $N\quad s\quad m^{ -2 }$

C- $km^{ -2 }\quad s$

D- $N\quad m^{ -2 }$

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**Hint:**Try to write the equation for viscous force. From that, we can calculate the units of the viscosity coefficient. Viscosity is the resistance force offered by the walls of the container to the flow of fluid.

**Complete answer:**

We know that the viscosity of a fluid is the resistance to the flow of fluid. It is the resistance between the layers of the fluids. Which decreases the velocity of the fluid. Viscosity acts along the tangential direction to the fluid flow. Fluid velocity will increase gradually as we move towards the centre of the fluid flow.

The viscous force will be proportional to the gradient of velocity and it will also be proportional to the area of the container. Assuming some constant we can write the formula of viscous force as:

\[F\quad =\quad \eta A\dfrac { dv }{ dx }\]

From this equation, we can get units of viscosity coefficient.

\[\eta\quad =\quad \dfrac { F }{ A } \dfrac { dv }{ dx } \]

Units of force F will be N, units of the area will be ${ m }^{ 2 }$, units of $\dfrac { dx }{ dv }$ will be the same as that of units of time which is s.

Units of viscosity coefficient $\eta \quad =\quad \dfrac { N }{ { m }^{ 2 } } s\quad =\quad Nm^{ -2 }\quad s$

**Therefore, option B is correct.**

**Note:**Due to viscosity every layer has different velocities in the fluid while flowing. Viscosity is the property of the fluid. It is different for different fluids. The viscosity of fluids changes with a change in temperature.