Question

A spherical ball of density $\text{ρ}$ and radius $0.003m$ is dropped into a tube containing a viscous fluid, filled up to the $0cm$ mark as shown in the figure. Viscosity of the fluid = $1.260N{m}^{-2}{s}^{-1}$ and its density ${\text{ρ}}_{\text{L}}$ = $\text{ρ}/2=1260kg{m}^{-3}$ . Assume the ball reaches a terminal speed by the $10cm$ mark. Find the time taken by the ball to traverse the distance between the $10cm$ and $20cm$ mark. [ $g$ = acceleration due to gravity = $10m{s}^{-2}$ ^​​ ]

• A. $2s$
• B. $3s$
• C. $5s$
• D. $1.5s$

Answer 1

Answer: (C)

Terminal Velocity:
$V_T=\frac{2}{9}\times \frac{{\left(\text{r}\right)}^2\left(\text{ρ}-{\left(\text{ρ}\right)}_{\text{L}}\right)\text{g}}{\text{η}}$
$\Rightarrow V_{\text{T}}=\frac{2}{9}\times \frac{{\left(3\times 10^{-3}\right)}^2\times 1260\times 10}{1\text{.}260}$
${\text{V}}_{\text{T}}=2\times 10^{-2}m{s}^{-1}$
$\Rightarrow {\text{V}}_{\text{T}}=2cm{s}^{-1}$
$\text{t}=\frac{10\text{cm}}{{\text{V}}_{\text{T}}}$
$\Rightarrow \text{t}=5\text{s}$