JEE Mains · Physics · STD 11 - Fluid mechanics
- JEE Mains 2024
- Hard
- MCQ
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 _______.
Pick an option to check your answer.
Answer & Solution
Correct Answer
(D) \(m g\left(1-\frac{\rho_0}{\rho}\right)\)
Step-by-step Solution
Detailed explanation
\(\mathrm{mg}-\mathrm{F}_{\mathrm{B}}-\mathrm{F}_{\mathrm{v}}=\mathrm{ma}\)
\(\mathrm{a}=0 \text { for constant velocity }\)
\(\mathrm{mg}-\mathrm{F}_{\mathrm{B}}=\mathrm{F}_{\mathrm{v}}\)
\(\mathrm{F}_{\mathrm{v}}=\mathrm{mg}-\mathrm{v} \rho_0 \mathrm{~g}=\mathrm{mg}-\frac{\mathrm{m}}{\rho} \rho_0 \mathrm{~g}=\mathrm{mg}\left(1-\frac{\rho_0}{\rho}\right)\)
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