# Terminal velocity of spherical body.

Gold Member
In our textbook, the equation for terminal velocity has been derived from Stokes' law and it comes down as follows,

vt = (mg)/6(pi)(eta)r

(r is the radius of the spherical body)

then, by putting the value of 'm' from m=(rho)V [where V = 4/3 * (pi)r3]

we get,
vt = 2(rho)gr2 / 9 (eta)

So in one equation, vt is directly related to r2, but in the other it is inversely related. Can someone please explain this to me.
Thak you.

The equation vt = (mg)/6(pi)(eta)r gives the relation between the terminal velocity and the radius for a spherical body of constant mass, that is, you are stretching the body by changing r (mass does not change).

However, in vt = 2(rho)gr2 / 9 (eta) the density is constant and hence as you change the radius, mass also changes.

Gold Member
So these are two equations for different situations?

Exactly.

Gold Member
Thanks for the help.