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If the terminal speed of a sphere of gold (density =19.5 { kg

Question

If the terminal speed of a sphere of gold (density $= 19.5 k g / m^{3}$ ) is $0.2 m / s$ in a viscous liquid (density $= 1.5 k g / m^{3}$ ), find the terminal speed of a sphere of silver (density $= 10.5 k g / m^{3}$ ) of the same size in the same liquid.

0.4 m / s

0.133 m / s

0.1 m / s

0.2 m / s

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If the terminal speed of a sphere of gold (density

= 19.5 k g / m^{3}

) is

0.2 m / s

in a viscous liquid (density

= 1.5 k g / m^{3}

), find the terminal speed of a sphere of silver (density

= 10.5 k g / m^{3}

) of the same size in the same liquid.

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Text solutionVerified

Terminal speed of spherical body in a viscous liquid is given by

v_{T} = \frac{2 r ^{2} ( ρ - σ ) g}{9 η}

where

ρ

density of substance of body and

σ

density of liquid.
From given data

\frac{v _{T} ( A g )}{v _{T} ( G o l d )} = \frac{ρ _{A g} - σ _{1}}{ρ _{g o l d} - σ _{1}}

\Rightarrow v_{T} (A g) = \frac{10.5 - 1.5}{19.5 - 1.5} \times 0.2 = \frac{9}{18} \times 0.2

= 0.1 m / s

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Question Text	If the terminal speed of a sphere of gold (density $= 19.5 k g / m^{3}$ ) is $0.2 m / s$ in a viscous liquid (density $= 1.5 k g / m^{3}$ ), find the terminal speed of a sphere of silver (density $= 10.5 k g / m^{3}$ ) of the same size in the same liquid.
Answer Type	Text solution:1
Upvotes	150