Consider two solid spheres P and Q each of density and diameters 1 cm and 0.5 cm, respectively. Sphere P is dropped into a liquid of density and viscosity poiseulles. Sphere Q is dropped into a liquid of density and viscosity poiseulles. The ratio of

Question

Consider two solid spheres P and Q each of density $8 {gm cm}^{- 3}$ and diameters 1 cm and 0.5 cm, respectively. Sphere P is dropped into a liquid of density $0.8 {gm cm}^{- 3}$ and viscosity $η = 3$ poiseulles. Sphere Q is dropped into a liquid of density $1.6 {gm cm}^{- 3}$ and viscosity $η = 2$ poiseulles. The ratio of the terminal velocities of P and Q is [2016]

Smart Achievers · Accepted Answer

(3)

$As we know, terminal velocity$

$V_{T} = \frac{2 r^{2}}{9 η} (ρ - σ) g$

$\frac{V_{P}}{V_{Q}} = \frac{\frac{2 r_{1}^{2} (σ - ρ_{1}) g}{9 η_{1}}}{\frac{2 r_{2}^{2} (σ - ρ_{2}) g}{9 η_{2}}}$

$= \frac{r_{1}^{2} (σ - ρ_{1})}{r_{2}^{2} (σ - ρ_{2})} \times \frac{η_{2}}{η_{1}}$

$= \frac{1^{2}}{{(0.5)}^{2}} [\frac{8 - 0.8}{8 - 1.6}] \times \frac{2}{3} = 3$

Solution

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Solution

Ans. (3) As we know, terminal velocity VT=2r29η(ρ-σ)g VPVQ=2r12(σ-ρ1)g9η12r22(σ-ρ2)g9η2 =r12(σ-ρ1)r22(σ-ρ2)×η2η1 =12(0.5)2[8-0.88-1.6]×23=3

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