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  • A solid ball of density and radius r falls vertically through a liquid of density <img alt="\mathrm{\rho_2}" src="/lat

A solid ball of density \mathrm{\rho_1} and radius r falls vertically through a liquid of density \mathrm{\rho_2}. Assume that the viscous force acting on the ball is \mathrm{F=k r v}, where k is a constant and v its velocity. What is the terminal velocity of the ball?

Option: 1

\mathrm{\frac{4 \pi \mathrm{gr}^2\left(\rho_1-\rho_2\right)}{3 \mathrm{k}}}


Option: 2

\mathrm{\frac{2 \pi r\left(\rho_1-\rho_2\right)}{3 g k}}


Option: 3

\mathrm{\frac{2 \pi g\left(\rho_1+\rho_2\right)}{3 g r^2 k}}


Option: 4

\mathrm{\text { None of these }}


Answers (1)

best_answer

\mathrm{\begin{aligned} & F_b+F_d=F_g \\ & \frac{4}{3} \pi r^3 \rho_2 g+k r v=\frac{4}{3} \pi r^3 \rho_1 g \end{aligned}}

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Rakesh

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