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:
JEE MAIN 2024, Diffcult
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$\mathrm{mg}-\mathrm{F}_{\mathrm{B}}-\mathrm{F}_{\mathrm{v}}=\mathrm{ma}$
$\mathrm{a}=0 \text { for constant velocity }$
$\mathrm{mg}-\mathrm{F}_{\mathrm{B}}=\mathrm{F}_{\mathrm{v}}$
$\mathrm{F}_{\mathrm{v}}=\mathrm{mg}-\mathrm{v} \rho_0 \mathrm{~g}=\mathrm{mg}-\frac{\mathrm{m}}{\rho} \rho_0 \mathrm{~g}=\mathrm{mg}\left(1-\frac{\rho_0}{\rho}\right)$
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