question_answer

The viscous force 'F' acting on a body of radius 'r' moving with a velocity ' \[\upsilon \]' in a medium of coefficient of viscosity ?\[\eta \]? is given by \[F=6\pi \eta r\upsilon \]. Check the correctness of the formula. 

Answer:

           \[[F]=[ML{{T}^{-2}}]\]                \[[6\pi \eta r\upsilon ]=[M{{L}^{-1}}{{T}^{-1}}][L][{{T}^{-1}}]=[ML{{T}^{-2}}]\] \[\therefore \] Dimensions of LHS = Dimensions of RHS. Hence the given formula for viscous force F is dimensionally correct.