A solid sphere of volume V experiences a viscous force F when descending with a speed v in a liquid. If another solid sphere of volume 27 V descends with the same speed v in the same liquid, it experiences a viscous force

Question

A solid sphere of volume V experiences a viscous force F when descending with a speed v in a liquid. If another solid sphere of volume 27 V descends with the same speed v in the same liquid, it experiences a viscous force (A) 12 F (B) 6 F (C) 9 F (D) F

Tardigrade Admin · Accepted Answer

Viscous force F=6 π η r v ⇒ F a r But r × V1 / 3 (hence V=(4/3) π r3 ) ⇒ (F'/F)=((V'/V))1 / 3 =((27 V/V))1 / 3=3 ∴ F'=3 F

Q. A solid sphere of volume $V$ experiences a viscous force $F$ when descending with a speed $v$ in a liquid. If another solid sphere of volume $27 V$ descends with the same speed $v$ in the same liquid, it experiences a viscous force

$12 F$

$6 F$

$9 F$

$F$

$3 F$

Viscous force $F = 6 π ηr v$
$\Rightarrow F a r$
But $r \times V^{1/3}$
(hence $V = \frac{4}{3} π r^{3}$ )
$\Rightarrow \frac{F ^{'}}{F} = (\frac{V ^{'}}{V})^{1/3}$
$= (\frac{27 V}{V})^{1/3} = 3$
$∴ F^{'} = 3 F$

Q. A solid sphere of volume V experiences a viscous force F when descending with a speed v in a liquid. If another solid sphere of volume 27V descends with the same speed v in the same liquid, it experiences a viscous force

12F

6F

9F

F

3F

Viscous force F=6πηrv ⇒Far But r×V1/3 (hence V=34​πr3 ) ⇒FF′​=(VV′​)1/3 =(V27V​)1/3=3 ∴F′=3F