Q85 / 120 · VITEEE 2016 · Physics
If the terminal speed of a sphere of gold (density $=19.5 \mathrm{~kg} / \mathrm{m}^{3}$ ) is $0.2 \mathrm{~m} / \mathrm{s}$ in a viscous liquid (density $=1.5 \mathrm{~kg} / \mathrm{m}^{3}$ ), find the terminal speed of a sphere of silver (density $=10.5 \mathrm{~kg} / \mathrm{m}^{3}$ ) of the same size in the same liquid
- A$0.4 \mathrm{~m} / \mathrm{s}$
- B$0.133 \mathrm{~m} / \mathrm{s}$
- Correct answerC$0.1 \mathrm{~m} / \mathrm{s}$
- D$0.2 \mathrm{~m} / \mathrm{s}$
Solution
Terminal velocity,
$$
\begin{array}{l}
v_{\mathrm{T}}=\frac{2 r^{2}\left(\mathrm{~d}_{1}-\mathrm{d}_{2}\right) \mathrm{g}}{9 \eta} \\
\frac{\mathrm{v}_{\mathrm{T}_{2}}}{0.2}=\frac{(10.5-1.5)}{(19.5-1.5)} \Rightarrow \mathrm{v}_{\mathrm{T}_{2}}=0.2 \times \frac{9}{18} \\
\therefore \mathrm{v}_{\mathrm{T}_{2}}=0.1 \mathrm{~m} / \mathrm{s}
\end{array}
$$
Hence, the correct answer is option: 'C'.