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A small ball of mass M and \rho density is dropped in a viscous liquid of density \rho_o. After some time, the ball falls with a constant velocity. What is the viscous force on the ball?

Option: 1

\mathrm{F}=\mathrm{Mg}\left(1+\frac{\rho_0}{\rho}\right)


Option: 2

F=M g\left(1+\frac{\rho}{\rho_0}\right)


Option: 3

\mathrm{F}=\mathrm{Mg}\left(1-\frac{\rho_0}{\rho}\right)


Option: 4

\mathrm{F}=\mathrm{Mg}\left(1 \pm \rho \rho_0\right)


Answers (1)

best_answer

At terminal velocity, net force on the ball is Zero.

\begin{aligned} & M g=f+B \\ & \Rightarrow M g=f+V_{\text {ball }} \rho_o g\\ &\text{Volume of ball} =\frac{M}{\rho}\\ &\text{From eq (i)}\Lambda ,\\ & M g=f+\frac{M}{\rho} \rho_o g \\ & \Rightarrow f=M g-\frac{M}{\rho} \rho_o g \\ & \Rightarrow f=M g\left(1-\frac{\rho_o}{\rho}\right) \end{aligned}

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Gaurav

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