A metal sphere of radius R, density ρ₁ moves with terminal velocity V₁ through a liquid of density σ. Another sphere of same radius but density ρ₂ moves through same liquid. Its terminal velocity is V₂. The ratio V₁: V₂ is (a) (ρ₂ + σ): (ρ₁ - σ) (b) (ρ₁ + σ): (ρ₂ - σ) (c) (ρ₂ - σ): (ρ₁ - σ) (d) (ρ₁ - σ): (ρ₂ - σ)

Answer: (d). v = (2R²(ρ - σ)g)/(9η); same R, liquid: v ∝ (ρ - σ). V₁: V₂ = (ρ₁ - σ): (ρ₂ - σ) So the answer is (d).

A metal sphere of radius R, density ρ₁ moves with terminal velocity… | MHT CET 2024 (10 May, Shift 1)

Q27MHT CET 2024 · 10 MAY · SHIFT 1Medium

Terminal Velocity

A metal sphere of radius R, density $\rho_1$ moves with terminal velocity $\mathrm{V}_1$ through a liquid of density $\sigma$ . Another sphere of same radius but density $\rho_2$ moves through same liquid. Its terminal velocity is $\mathrm{V}_2$ . The ratio $\mathrm{V}_1 : \mathrm{V}_2$ is

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Answer: (d)

$v = \dfrac{2R^2(\rho - \sigma)g}{9\eta}$ ; same $R$ , liquid: $v \propto (\rho - \sigma)$ .
$V_1 : V_2 = (\rho_1 - \sigma) : (\rho_2 - \sigma)$
So the answer is (d).

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Terminal Velocity question from MHT CET 2024 (10 May, Shift 1)

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