Question

The SI unit of coefficient of viscosity is:
(i) $N{s^{ - 1}}{m^{ - 2}}$
(ii) $Ns{m^{ - 2}}$
(iii)$N{s^{ - 2}}{m^{ - 2}}$
(iv)$N{s^{ - 1}}{m^{ - 3}}$

Answer 1

Hint:
To find the SI units of any quantity we have to write its formula in terms of other quantities and then find the SI units of the given quantity. The coefficient of viscosity is defined as the tangential force acting per unit area of the fluid (or liquid) divided by the velocity gradient (velocity divided by the distance between the two moving layers of the fluid) provided the flow of liquid is streamlined.
The formula used: The symbol for the coefficient of viscosity is ‘$\eta $ ‘. It is given by the following formula:
$\eta = \dfrac{{Fr}}{{Av}}$
Here, F is force, r is the distance between layers, A is area and v is velocity.


Complete answer:
According to definition the formula for the coefficient of viscosity can be written as:
$\eta = \dfrac{{Fr}}{{Av}}$
The SI units of force, F are Newton (N)
The SI units of distance, r are meter (m)
The SI units of area, A are meter squared (${m^2}$ )
The SI units of velocity, v are meter per second $(m{s^{ - 1}})$
Now, by putting these units in the formula for coefficient of viscosity we get,
$\
  \eta = \dfrac{{N.m}}{{{m^2}.m{s^{ - 1}}}} \\
  \eta = N{m^{ - 2}}s \\
\ $

Hence, the SI units of coefficient of viscosity will be $N{m^{ - 2}}s$ or $Ns{m^{ - 2}}$. So option (ii) is correct.

Additional information:As force per unit area i.e. $N{m^{ - 2}}$ is pressure. It can be written as pascal. So, the SI units of $\eta $ can also be written as Pascal second. CGS units of $\eta $ are poise.


Note:
There is also an alternative method to find out SI units of any quantity. It is by converting the quantities in the formula to their dimensions and then finding out the dimensions of the given quantity.