If the terminal speed of a sphere of gold (density = 19.5 kg/m³) is 0.2 m/s in a viscous liquid (density = 1.5 kg/m³, find the terminal speed of a sphere of silver (density = 10.5 kg/m³) 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: (c). Same size and liquid: v ∝ (ρ - σ). (vs)/(vg) = (10.5 - 1.5)/(19.5 - 1.5) = 9/18 = 1/2 vs = 0.2 × 1/2 = 0.1 m/s So the answer is (c) 0.1 m/s.

If the terminal speed of a sphere of gold (density = 19.5 kg/m³) is… | JEE Main 2006 (AIEEE)

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Terminal Velocity

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 of a sphere of silver (density $= 10.5\ kg/m^{3}$ ) of the same size in the same liquid

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Answer: (c)

Same size and liquid: $v \propto (\rho - \sigma)$ .
$\dfrac{v_s}{v_g} = \dfrac{10.5 - 1.5}{19.5 - 1.5} = \dfrac{9}{18} = \dfrac{1}{2}$
$v_s = 0.2 \times \frac{1}{2} = 0.1$ m/s
So the answer is (c) $0.1$ m/s.

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