Question

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

• A. $0.4\, m/s$
• B. $0.133\, m/s$
• C. $0.1\, m/s$
• D. $0.2\, m/s$

Answer 1

Answer: (C)

Terminal speed of spherical body in a viscous liquid is given by
$v_{r}=\frac{2r^{2}\left(\rho-\sigma\right)g}{9\eta}$
where $\rho =$ density of substance of body
$\sigma=$density of liquid
From given data
$\frac{v_{T}\left(Ag\right)}{v_{T}\left(Gold\right)}=\frac{\rho_{Ag}-\sigma_{l}}{\rho_{Gold}-\sigma_{l}}$
$\Rightarrow v_{T}\left(Ag\right)=\frac{10.5-1.5}{19.5-1.5}\times0.2=\frac{9}{18}\times0.2$
$=0.1\,m/s$