Dimensions of coefficient of viscosity are

The correct option is [ML⁻¹T⁻¹].

To find the dimensional formula of the coefficient of viscosity, we can use Newton's formula for viscous force:

$F=\eta A\frac{dv}{dx}$

Where:
- $F$ is the viscous force.
- $\eta$ is the coefficient of viscosity.
- $A$ is the area of the contact surface.
- $\frac{dv}{dx}$ is the velocity gradient.

Rearranging the formula to solve for the coefficient of viscosity ($\eta$):

$\eta =\frac{F}{A\left(\frac{dv}{dx}\right)}$

Now, let's write down the dimensional formulas of the individual physical quantities involved:

1. Dimensional formula of Force ($F$):

$\left[F\right]=\left[ML{T}^{-2}\right]$

2. Dimensional formula of Area ($A$):

$\left[A\right]=\left[L^2\right]$

3. Dimensional formula of velocity gradient ($\frac{dv}{dx}$):

$\left[\frac{dv}{dx}\right]=\frac{\left[L{T}^{-1}\right]}{\left[L\right]}=\left[T^{-1}\right]$

Substituting these dimensions into the expression for $\eta$:

$\left[\eta \right]=\frac{\left[ML{T}^{-2}\right]}{\left[L^2\right]\left[T^{-1}\right]}$

Simplifying the expression:

$\left[\eta \right]=\left[M{L}^{1-2}{T}^{-2-(-1)}\right]$

$\left[\eta \right]=\left[M{L}^{-1}{T}^{-1}\right]$

Thus, the dimensional formula of the coefficient of viscosity is [ML⁻¹T⁻¹].