A sphere of mass M and radius R is falling in a viscous fluid. The terminal velocity attained by the falling object will be proportional to

Question

A sphere of mass M and radius R is falling in a viscous fluid. The terminal velocity attained by the falling object will be proportional to (A) MR2 (B) MR (C) M/R (D) M/R2

Tardigrade Admin · Accepted Answer

V 0=(2/9) ( R 3(ρ-ρ prime) g / R η ) But m =(4/3) π R 3 ρ or m propto R 3 V0 propto (M/R)

Q. A sphere of mass $M$ and radius $R$ is falling in a viscous fluid. The terminal velocity attained by the falling object will be proportional to

$M R^{2}$

$MR$

$M / R$

$M / R^{2}$

$< b r / > V_{0} = \frac{2}{9} \frac{R ^{3} ( ρ - ρ ^{'} ) g}{R η} < b r / >$
But $m = \frac{4}{3} π R^{3} ρ$ or $m \propto R^{3}$
$< b r / > V_{0} \propto \frac{M}{R} < b r / >$

Q. A sphere of mass M and radius R is falling in a viscous fluid. The terminal velocity attained by the falling object will be proportional to

MR2

MR

M/R

M/R2