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JEE Main 202431 JanuaryEvening Shift

Exam: JEE Main
Year: 2024
Date: 31 January
Shift: Evening Shift
Subject: Physics
Chapter: Mechanical Properties of Fluids

JEE Main 2024 · 31 January · Evening Shift · Physics · Mechanical Properties of Fluids

A small spherical ball of radius r , falling through a viscous...

A small spherical ball of radius

r

, falling through a viscous medium of negligible density has terminal velocity

v

. Another ball of the same mass but of radius

2r

, falling through the same viscous medium will have terminal velocity:

Options

A $\dfrac{v}{2}$
B $\dfrac{v}{4}$
C $4v$
D $2v$

Correct answer

A. $\dfrac{v}{2}$

Step-by-step solution

Ignoring buoyancy force, we can write terminal velocity as

$mg = 6\piηrv$

$⇒ v ∝ \dfrac{1}{r}$ (as mass is constant)

Now, $\dfrac{v}{v '} = \dfrac{r '}{r}$

$\text{As}r ' = 2r$

So $v ' = \dfrac{v}{2}$

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