The terminal velocity \(v\) of a spherical ball of lead of radius \(R\) falling through a viscous liquid…
The terminal velocity \(v\) of a spherical ball of lead of radius \(R\) falling through a viscous liquid varies with \(R\) such that
\(\frac{v}{R}=\) constant
\(v R=\) constant
\(v=\) constant
\(\frac{v}{R^2}=\) constant
Solution
Terminal velocity of spherical ball falling through viscous liquid is given as
\(v=\frac{2}{9} \times \frac{R^2(\rho-\sigma) g}{\eta}\) ...(i)
where, \(R=\) radius of ball, \(\rho=\) density of ball, \(\sigma=\) density of liquid and \(\eta=\) coefficient of viscosity.
From Eq. (i),
\(\frac{v}{R^2}=\frac{2(\rho-\sigma) g}{9 \eta}=\text { constant }\)