Question

If the terminal speed of a sphere of gold (density $=19.5{\text{kg/m}}^3$) is $0.2\text{m/s}$ in a viscous liquid (density $=1.5{\text{kg/m}}^3$), find the terminal speed of a sphere of silver (density $=10.5{\text{kg/m}}^3$) of the same size in the same liquid

• A. $0.4\text{m/s}$
• B. $0.133\text{m/s}$
• C. $0.1\text{m/s}$
• D. $0.2\text{m/s}$

Answer 1

The correct option is C $0.1\text{m/s}$

$V_T=\frac{2r^2(d_1-d_2)g}{9\eta }$

$\frac{V_{T_2}}{0.2}=\frac{(10.5-1.5)}{(19.5-1.5)}\Rightarrow V_{T_2}=0.2\times \frac{9}{18}$

$\therefore V_{T_2}=0.1\text{m/s}$