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 s - Physics MCQ AIEEE 2006 2026 | ExamTest.live

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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.

Solution & Step-by-step Explanation

Terminal velocity v_{t} = \frac{2 r ^{2} g ( ρ _{s} - ρ _{l} )}{9 η} .For spheres of the same size in the same liquid: v_{t} \propto (ρ_{s} - ρ_{l}) . \frac{v _{s i l v er}}{v _{g o l d}} = \frac{ρ _{s i l v er} - ρ _{l}}{ρ _{g o l d} - ρ _{l}} \frac{v _{s i l v er}}{0.2} = \frac{10.5 - 1.5}{19.5 - 1.5} = \frac{9}{18} = 1/2 v_{s i l v er} = 0.2 \times 0.5 = 0.1 m/s

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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.

0.2 m/s

0.4 m/s

0.133 m/s

0.1 m/s

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