Question

If the terminal speed of a sphere of gold (density $=19.5\, kg / m ^{3}$ ) is $0.2\, m / s$ in 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
$v_{T}=\frac{2 r^{2}(\rho-\sigma) g}{9 \eta}$
where $\rho=$ density of substance of body
and $\sigma=$ density of liquid .
From given data
$\frac{v_{T}( Ag )}{v_{T}( Gold )} =\frac{\rho_{ Ag }-\sigma_{l}}{\rho_{ Gold }-\sigma_{l}} $
$\Rightarrow v_{T}( Ag ) =\frac{10.5-1.5}{19.5-1.5} \times 0.2$
$=\frac{9}{18} \times 0.2$
$=0.1\, m / s$