If the terminal speed of a sphere of gold (density= $19.5 \frac{k g}{m^{3}}$ ) is $8 \frac{m}{s}$ in a viscous liquid (density = $1.5 \frac{k g}{m^{3}}$ ). Find the terminal speed of a sphere of silver (density = $10.5 \frac{k g}{m^{3}}$ ) of the same size in the same liquid

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$0.4 \frac{m}{s}$

$4 \frac{m}{s}$

$0.1 \frac{m}{s}$

$0.2 \frac{m}{s}$

answer is B.

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Detailed Solution

Terminal speed of spherical body in a viscous liquid is given by $V_{T} = \frac{2 r^{2} (ρ - σ)}{9 η} g$

$∴ \frac{v_{T} (A g)}{v_{T} (g o l d)} = \frac{ρ_{A g} - σ_{1}}{ρ_{g o l d} - σ_{1}} = | \frac{10.5 - 1.5}{19.5 - 1.5}) \Rightarrow V_{T} (A g) = \frac{9}{18} \times 8 = 4 m / s$

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