A ball of mass m and radius r is released in viscous liquid. The value of its terminal velocity is proportional to

Question

A ball of mass m and radius r is released in viscous liquid. The value of its terminal velocity is proportional to (A) (1/r) only (B) m / r (C) ( m / r )1 / 2 (D) m only

Tardigrade Admin · Accepted Answer

Terminal velocity (v)=(2/9) (r2(ρ-σ) g/η) v=(2 r2 ρ(1-(σ/ρ)) g/9 η)=(2 r3 ρ(1-(σ/ρ)) g/9 r η) v propto (m/r) (m=(4/3) π r3 ρ) (m propto r3 ρ)

Q. A ball of mass $m$ and radius $r$ is released in viscous liquid. The value of its terminal velocity is proportional to

$\frac{1}{r}$ only

$m / r$

$(m / r)^{1/2}$

$m$ only

Terminal velocity $(v) = \frac{2}{9} \frac{r ^{2} ( ρ - σ ) g}{η}$
$v = \frac{2 r ^{2} ρ ( 1 - \frac{σ}{ρ} ) g}{9 η} = \frac{2 r ^{3} ρ ( 1 - \frac{σ}{ρ} ) g}{9 rη}$
$v \propto \frac{m}{r}$
$(m = \frac{4}{3} π r^{3} ρ)$
$(m \propto r^{3} ρ)$

Q. A ball of mass m and radius r is released in viscous liquid. The value of its terminal velocity is proportional to

r1​ only

m/r

(m/r)1/2

m only