Properties of Matter 4 Question 12
14. Consider two solid spheres $P$ and $Q$ each of density $8 \mathrm{gm} \mathrm{cm}^{-3}$ and diameters $1 \mathrm{~cm}$ and $0.5 \mathrm{~cm}$, respectively. Sphere $P$ is dropped into a liquid of density $0.8 \mathrm{gm} \mathrm{cm}^{-3}$ and viscosity $\eta=3$ poisculles. Sphere $Q$ is dropped into a liquid of density $1.6 \mathrm{gm} \mathrm{cm}^{-3}$ and viscosity $\eta=2$ poiseulles. The ratio of the terminal velocities of $P$ and $Q$ is
(2016 Adv.)
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Answer:
Correct Answer: 14. 3
Solution:
- Terminal velocity is given by
$$ \begin{aligned} v _T & =\frac{2}{9} \frac{r^{2}}{\eta}(d-\rho) g \\ \frac{v _P}{v _Q} & =\frac{r _P^{2}}{r _Q^{2}} \times \frac{\eta _Q}{\eta _P} \times \frac{\left(d-\rho _P\right)}{\left(d-\rho _Q\right)} \\ & =\left(\frac{1}{0.5}\right) \times\left(\frac{2}{3}\right) \times \frac{(8-0.8)}{(8-1.6)} \\ & =4 \times \frac{2}{3} \times \frac{7.2}{6.4}=3 \end{aligned} $$
