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 (in $m/s$) of a sphere of silver (density $= 10.5\ kg/m^3$) of the same size in the same liquid ...... $m/s$
AIEEE 2006,AIIMS 2008, Medium
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Terminal velocity, ${v_T} = \frac{{2{r^2}\left( {{d_1} - {d_2}} \right)g}}{{9\eta }}$
$\frac{{{v_{{T_2}}}}}{{0.2}} = \frac{{\left( {10.5 - 1.5} \right)}}{{\left( {19.5 - 1.5} \right)}} \Rightarrow {v_{{T_2}}} = 0.2 \times \frac{9}{{18}} = 0.1\,m/s$
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