The terminal velocity ( v _ t ) of the spherical rain drop depends on the radius (r) of the spherical rain drop as

Correct answer: B. r ^ 2 The terminal velocity of a sphere of radius r and density ρ , immersed in a liquid of density σ and viscosity η is given by v _ T = (2)/(9) (ρ - σ) r ^ 2 g η Hence, for spherical raindrop, v _ T ∝ r ^ 2 .

JEE Main 202225 JuneMorning Shift

Exam: JEE Main
Year: 2022
Date: 25 June
Shift: Morning Shift
Subject: Physics
Chapter: Mechanical Properties of Fluids

JEE Main 2022 · 25 June · Morning Shift · Physics · Mechanical Properties of Fluids

The terminal velocity ( v _ t ) of the spherical rain drop depends...

The terminal velocity

\left({v}_{t}\right)

of the spherical rain drop depends on the radius

\left(r\right)

of the spherical rain drop as

Options

A $r$
B ${r}^{2}$
C $\dfrac{1}{r}$
D $\dfrac{1}{{r}^{2}}$

Correct answer

B. ${r}^{2}$

Step-by-step solution

The terminal velocity of a sphere of radius $r$ and density $ρ$ , immersed in a liquid of density $\sigma$ and viscosity $η$ is given by ${v}_{T} = \dfrac{2}{9}\dfrac{\left(ρ - \sigma\right){r}^{2}g}{η}$

Hence, for spherical raindrop, ${v}_{T} ∝ {r}^{2}$ .

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