Question

What is the dimensional formula of co-efficient of viscosity?

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

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,
$\left[\eta\right]=\frac{\left[M^{1} L^{1} T^{- 2}\right] \left[M^{0} L^{1} T^{0}\right]}{\left[M^{0} L^{2} T^{0}\right] \left[M^{0} L^{1} T^{- 1}\right]}=\left[M^{1} L^{- 1} T^{- 1}\right]$