A small ball of mass m and density is dropped in a viscous liquid of density _0 . After sometime, the ball falls with constant velocity. The viscous force on the ball is :

Correct answer: D. m g (1-( _0)/( ))_ mg-F_ B -F_ v =ma a=0 for constant velocity aligned & m g-F_B=F_v & F_v=m g-v _0 g=m g-(m)/( ) _0 g=m g(1-( _0)/( )) aligned

JEE Main 20246 AprilMorning Shift

Exam: JEE Main
Year: 2024
Date: 6 April
Shift: Morning Shift
Subject: Physics
Chapter: Mechanical Properties of Fluids

JEE Main 2024 · 6 April · Morning Shift · Physics · Mechanical Properties of Fluids

A small ball of mass m and density is dropped in a viscous liquid...

A small ball of mass

m

and density

\rho

is dropped in a viscous liquid of density

\rho_0

. After sometime, the ball falls with constant velocity. The viscous force on the ball is :

Options

A $m g\left(1-\rho \rho_0\right)$
B $m g\left(1+\frac{\rho}{\rho_0}\right)$
C $m g\left(\frac{\rho_0}{\rho}-1\right)$
Dm g $\left(1-\frac{\rho_0}{\rho}\right)_{\nabla}$

Correct answer

D. m g $\left(1-\frac{\rho_0}{\rho}\right)_{\nabla}$

Step-by-step solution

\mathrm{mg}-\mathrm{F}_{\mathrm{B}}-\mathrm{F}_{\mathrm{v}}=\mathrm{ma} \mathrm{a}=0

for constant velocity

\begin{aligned} & m g-F_B=F_v \\ & F_v=m g-v \rho_0 g=m g-\frac{m}{\rho} \rho_0 g=m g\left(1-\frac{\rho_0}{\rho}\right) \end{aligned}

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