JEE Mains · Physics · STD 11 - 9.1 fluid mechanics
A small ball of mass \(M\) and density \(\rho\) is dropped in a viscous liquid of density \(\rho_0\). After some time, the ball falls with a constant velocity. What is the viscous force on the ball ?
- A \(F=\mathrm{Mg}\left(1-\frac{\rho_0}{\rho}\right)\)
- B \(F=M g\left(1+\frac{\rho}{\rho_0}\right)\)
- C \(F=\mathrm{Mg}\left(1+\frac{\rho_0}{\rho}\right)\)
- D \(F=\mathrm{Mg}\left(\mathrm{l} \pm \rho \rho_0\right)\)
Answer & Solution
Correct Answer
(A) \(F=\mathrm{Mg}\left(1-\frac{\rho_0}{\rho}\right)\)
Step-by-step Solution
Detailed explanation
For constant velocity \(F_{\text {net }}=0\) \(\mathrm{F}_{\mathrm{vis}}+\rho_0 \mathrm{vg}=\rho \mathrm{vg}\) \(\mathrm{F}_{\mathrm{vis}}=\left(\rho-\rho_0\right) \mathrm{vg}\) \(=\rho \mathrm{vg}\left(1-\frac{\rho_0}{\rho}\right)\)…
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