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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 $ρ$ ₂is dropped in the same liquid, its terminal velocity will be

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$(\frac{ρ_{1}}{ρ_{2}}) v_{1}$

$(\frac{ρ_{2}}{ρ_{1}}) V_{1}$

$(\frac{ρ_{2} - σ}{ρ_{1} - σ}) V_{1}$

$(\frac{ρ_{1} - σ}{ρ_{2} \dots σ}) V_{1}$

answer is A.

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Detailed Solution

Hero $6 {πηRv}_{1} = \frac{4}{3} {πR}^{3} (ρ_{1} - σ)$
and $6 {πηRv}_{2} = \frac{4}{3} {πR}^{3} (ρ_{2} - σ)$
$∴ \frac{v_{2}}{v_{1}} = \frac{(ρ_{2} - σ)}{(ρ_{1} - σ)}$

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