Two small spherical metal balls, having equal masses, are made from materials of densities ρ1 and ρ2(ρ1 = 8π2) and have radii of 1mm and 2mm, respectively. They are made to fall vertically (from rest) in a viscous medium whose coefficient of viscosity equals η and whose density is 0.1 ρ2. The ratio of their terminal velocities would be :

Question

Two small spherical metal balls, having equal masses, are made from materials of densities ρ1 and ρ2(ρ1 = 8π2) and have radii of 1mm and 2mm, respectively. They are made to fall vertically (from rest) in a viscous medium whose coefficient of viscosity equals η and whose density is 0.1 ρ2. The ratio of their terminal velocities would be : (A) (79/72) (B) (19/36) (C) (39/72) (D) (79/36)

Tardigrade Admin · Accepted Answer

<img class="img-fluid question-image" alt="image" src="https://cdn.tardigrade.in/img/question/physics/58661e353100b567f5d065706ab58399-.png" /> vr = (2r2(σ - ρ)g/9η) (v1/v2) = ((r1/r2))2 ((σ1 - ρ)/(σ2 - ρ)) = ((1/2))2 ((8ρ2 - 0.1 ρ2/ρ2 - 0.1 ρ2)) = (79/36)

$\frac{79}{72}$

$\frac{19}{36}$

$\frac{39}{72}$

$\frac{79}{36}$

$v_{r} = \frac{2 r ^{2} ( σ - ρ ) g}{9 η}$
$\frac{v _{1}}{v _{2}} = (\frac{r _{1}}{r _{2}})^{2} \frac{( σ _{1} - ρ )}{( σ _{2} - ρ )}$
$= (\frac{1}{2})^{2} (\frac{8 ρ _{2} - 0.1 ρ _{2}}{ρ _{2} - 0.1 ρ _{2}}) = \frac{79}{36}$

7279​

3619​

7239​

3679​

vr​=9η2r2(σ−ρ)g​ v2​v1​​=(r2​r1​​)2(σ2​−ρ)(σ1​−ρ)​ =(21​)2(ρ2​−0.1ρ2​8ρ2​−0.1ρ2​​)=3679​

$\frac{79}{72}$

$\frac{19}{36}$

$\frac{39}{72}$

$\frac{79}{36}$

$v_{r} = \frac{2 r ^{2} ( σ - ρ ) g}{9 η}$
$\frac{v _{1}}{v _{2}} = (\frac{r _{1}}{r _{2}})^{2} \frac{( σ _{1} - ρ )}{( σ _{2} - ρ )}$
$= (\frac{1}{2})^{2} (\frac{8 ρ _{2} - 0.1 ρ _{2}}{ρ _{2} - 0.1 ρ _{2}}) = \frac{79}{36}$