A steel ball of radius 6 mm has a terminal speed of $12 \mathrm{cms}^{-1}$ in a viscous liquid. What will be the terminal speed of a steel ball of radius 3 mm in the same liquid?

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Aicharya · Accepted Answer

Terminal speed, $v=\frac{2 r^2 g\left(ho-ho_Light)}{9 \eta}$ Since density of balls and liquid remains the same, $\begin{aligned} & 	herefore \quad \frac{\mathrm{v}_{\mathrm{A}}}{\mathrm{v}_{\mathrm{B}}}=\left(\frac{\mathrm{r}_{\mathrm{A}}}{\mathrm{r}_{\mathrm{B}}}ight)^2=\left(\frac{6}{3}ight)^2=4 \ & 	herefore \quad \mathrm{v}_{\mathrm{B}}=\frac{\mathrm{v}_{\mathrm{A}}}{4}=\frac{12}{4}=3 \mathrm{cms}^{-1} \end{aligned}$

A steel ball of radius 6 mm has a terminal speed of $12 \mathrm{cms}^{-1}$ in a viscous liquid. What will be…

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