Question

Using dimensional analysis find out the dimensional formula for the coefficient of viscosity.

• A. Dimensional formula: $\left[{\text{M}}^1{\text{L}}^{-1}{\text{T}}^{-1}\right]$
• B. Dimensional formula: $\left[{\text{M}}^2{\text{L}}^{-3}{\text{T}}^{-1}\right]$
• C. Dimensional formula: $\left[{\text{M}}^{-4}{\text{L}}^1{\text{T}}^{-2}\right]$
• D. Dimensional formula: $\left[{\text{M}}^{-1}{\text{L}}^3{\text{T}}^{-2}\right]$

Answer 1

Answer: (A)

Coefficient of viscosity $\left(\eta \right)=\frac{Fx}{Av}$
F = tangential Force,
A = Area, x = distance between the layers,
v = velocity.
Dimensional Formula of Force $=M^1{L}^1{T}^{-2}$
Dimensional Formula of Area $=M^0{L}^2{T}^0$
Dimensional Formula of distance $=M^0{L}^1{T}^0$
Dimensional Formula of velocity $=M^0{L}^1{T}^{-1}$
Putting these values in above equation we get,
$\left[\eta \right]=\frac{\left[M^1{L}^1{T}^{-2}\right]\left[M^0{L}^1{T}^0\right]}{\left[M^0{L}^2{T}^0\right]\left[M^0{L}^1{T}^{-1}\right]}=\left[M^1{L}^{-1}{T}^{-1}\right]$