Question

The force F on a sphere of radius r moving in a medium with velocity v given by $ F=6\pi \,\eta rv $ . The dimensions of r) are :

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

Answer 1

Answer: (D)

Viscous force on a sphere of radius r is $ F=6\pi \eta rv $ $ \therefore $ $ \eta =\frac{F}{6\pi rv} $ $ |\eta |=\frac{|F|}{|r|\,|v|}=\frac{[ML{{T}^{-2}}]}{[L][L{{T}^{-1}}]}=[M{{L}^{-1}}{{T}^{-1}}] $ NOTE: The above expression is the Stokes law.