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Q.

If the terminal speed of a sphere of gold (density =19.5Kg / m³ )is 0.2 m/s in a viscous liquid (density =1.5kg / m³), find the terminal speed of a sphere of silver (density =10.5kg / m³ ) of the same size in the same liquid

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a

0.4 m/s

b

0.133 m/s

c

0.1 m/s

d

0.2 m/s

answer is C.

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Detailed Solution

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Density of gold, $ρ_{G} = 19 .5 kg / m^{3}$
Density of silver, $ρ_{5} = 10 .5 kg / m^{3}$
Density of liquid, $σ = 1 .5 kg / m^{3}$
Terminal velocity, $v_{T} = \frac{2 r^{2} (ρ - σ) g}{9 η}$
$∴ \frac{v_{T_{2}}}{0 .2} = \frac{(10 .5 - 1 .5)}{(19 .5 - 1 .5)} \Rightarrow v_{T_{2}} = 0 .2 \times \frac{9}{18} ∴ v_{T_{2}} = 0 .1 m / s$

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If the terminal speed of a sphere of gold (density =19.5Kg / m3 )is 0.2 m/s in a viscous liquid (density =1.5kg / m3 ), find the terminal speed of a sphere of silver (density =10.5kg / m3 ) of the same size in the same liquid