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A sphere of radius R and density $ρ_{1}$ is dropped in a liquid of density $σ$ . Its terminal velocity is $v_{1}$ . If another sphere of radius R and density $ρ_{2}$ is dropped in the same liquid, its terminal velocity will be:

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$(\frac{ρ_{2} - σ}{ρ_{1} - σ}) v_{1}$

$(\frac{ρ_{1} - σ}{ρ_{2} - σ}) v_{1}$

$(\frac{ρ_{1}}{ρ_{2}}) v_{1}$

$(\frac{ρ_{2}}{ρ_{1}}) v_{1}$

answer is A.

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Detailed Solution

$6 {πηRv}_{1} = \frac{4}{3} {πR}^{3} (ρ_{1} - σ)$

$6 {πηRv}_{2} = \frac{4}{3} {πR}^{3} (ρ_{2} - σ)$

$∴ \frac{v_{2}}{v_{1}} = (\frac{ρ_{2} - σ}{ρ_{1} - σ})$

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