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 $\left(\eta\right)=\frac{F x}{A v}$
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,
$\left[\eta\right]=\frac{\left[M^{1} L^{1} T^{- 2}\right] \left[M^{0} L^{1} T^{0}\right]}{\left[M^{0} L^{2} T^{0}\right] \left[M^{0} L^{1} T^{- 1}\right]}=\left[M^{1} L^{- 1} T^{- 1}\right]$