Question

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

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

Answer 1

The correct option is C $0.1m/s$

Terminal speed of spherical body in a viscous liquid is given by
$v_T=\frac{2r^2(\rho -\sigma )g}{9\eta }$
where $\rho$ density of substance of body and $\sigma$ density of liquid.
From given data
$\frac{v_T\left(Ag\right)}{v_T\left(Gold\right)}=\frac{{\rho }_{Ag}-{\sigma }_1}{{\rho }_{gold}-{\sigma }_1}$
$\Rightarrow v_T\left(Ag\right)=\frac{10.5-1.5}{19.5-1.5}\times 0.2=\frac{9}{18}\times 0.2$ $=0.1m/s$