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If the terminal speed of a sphere of gold $(d e n s i t y = 19.5 k g / m^{3})$ is $0.2 m / s$ in a viscous liquid $(d e n s i t y = 1.5 k g / m^{3})$ , find the terminal speed of a sphere of silver $(density = 10.5 kg / m^{3})$ of the same size in the same liquid

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$0.1 m / s$

$0.2 m / s$

$0.4 m / s$

$0.133 m / s$

answer is C.

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Detailed Solution

Terminal velocity, $v_{T} = \frac{2 r^{2} (ρ - σ) g}{9 η}$

$∴ \frac{v_{T_{2}}}{0.2} = \frac{(10.5 - 1.5)}{(19.5 - 1.5)} \Rightarrow v_{T_{2}} = 0.2 \times \frac{9}{18} = 0.1 m / s$

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