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If the terminal speed of a sphere of gold (density $19.5 \,kg / m ^2$ ) 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 is ............ $m / s$
$0.2$
$0.4$
$0.1$
$0.133$
Solution
(c)
$V_{\text {terminal }}=\frac{2 a^2}{9 \eta}(\rho-\sigma) g$ $\left\{\begin{array}{l}\text { Where } \\ \rho=\text { density of material } \\ \sigma=\text { density of liquid }\end{array}\right.$
$\Rightarrow V_T \propto(\rho-\sigma)$
$\Rightarrow \frac{V_{T_1}}{V_{T_2}}=\frac{\rho_{\text {gold }}-\sigma_{\text {liquid }}}{\rho_{\text {silver }}-\sigma_{\text {liquid }}}$
$\Rightarrow \frac{0.2}{V}=\frac{19.5-1.5}{10.5-1.5}$ $\left\{\begin{array}{l}\text { Given, } \\ V_{T_1}=0.2 \,m / s \\ V_{T_2}=V=? \\ \rho_{\text {gold }}=19.5 \,kg / m ^3 \\ \sigma_{\text {liquid }}=1.5 \,kg / m ^3 \\ \rho_{\text {silver }}=10.5 \,kg / m ^3\end{array}\right.$
$\Rightarrow V=0.1 \,m / s$
