Answer to Question #244618 in Mechanics | Relativity for Ubaid

Question

A sphere of radius r moving with a velocity v under streamline conditions in a viscous fluid experiences a retarding force, F, given by F=krv, Where K is a constant. Derive the S.I unit and the physical dimension of k

Answer 1

We use the formula and we start to substitute all the units for F (Newton), r (meters) and velocity v (meters/second) to find:

$F=krv \\ \implies [N]=k[m][m/s ]=k[m^2/s] \\ \implies k=\cfrac{[N]}{[m^2/s]}=\cfrac{[Ns]}{[m^2]}=\cfrac{[(kgm/s^2)s]}{[m^2]} \\ \implies k=\bigg[\cfrac{kg}{ms} \bigg]$

In conclusion, the SI units for the constant k are $kg/(m\cdot s)$ or $Pa\cdot s$.

The dimensions of k will be $\dfrac{[Mass]}{[Length*Time]}$.

Reference:

• Sears, F. W., & Zemansky, M. W. (1973). University physics.