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If the terminal speed of a sphere of gold (density =19.5 kg m⁻³) is 0.2 m s⁻¹ 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.

Asked in AIEEE 2006 · Terminal velocity and its dependences

• (1) 0.2 m s⁻¹
• (2) 0.4 m s⁻¹
• (3) 0.133 m s⁻¹
• (4) 0.1 m s⁻¹

Step-by-step solution

Why the other options are wrong

• (1) comes from assumes the terminal speed depends only on the size, which would be true if the drag balanced nothing; it balances the apparent weight, and silver's is half that of gold.
• (2) comes from inverts the ratio, using (18)/9=2 in place of 9/(18)=1/2; the lighter sphere cannot fall faster.
• (3) comes from taking the ratio of the raw densities the wrong way about, 2/3 style, instead of the ratio of the density differences (10.5-1.5)/(19.5-1.5).

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