Fluid Mechanics

JEE Main level, single correct, medium

172 of 192

Question 172 of 192

A small ball of mass mm and density ρ\rho is dropped in a viscous liquid of density ρ0\rho_0. After sometime, the ball falls with constant velocity. The viscous force on the ball is :

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Answer: (D) mg(1−ρ0ρ)∇m g\left(1-\frac{\rho_0}{\rho}\right)_{\nabla}

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