An iron sphere of mass $20 imes 10^{-3} \mathrm{~kg}$ falls through a viscous liquid with terminal velocity $0.5 \mathrm{~ms}^{-1}$. The terminal velocity (in $\mathrm{ms}^{-1}$ ) of another iron sphere of mass $54 imes 10^{-2} \mathrm{~kg}$ is

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An iron sphere of mass $20 	imes 10^{-3} \mathrm{~kg}$ falls through a viscous liquid with terminal velocity $0.5 \mathrm{~ms}^{-1}$. The terminal velocity (in $\mathrm{ms}^{-1}$ ) of another iron sphere of mass $54 	imes 10^{-2} \mathrm{~kg}$ is

Aicharya · Accepted Answer

Terminal velocity, $v \propto r^2$ $\begin{aligned} 	ext { or } \quad \frac{v_1}{v_2} & =\left(\frac{r_1}{r_2}ight)^2=\left[\left(\frac{r_1}{r_2}ight)^3ight]^{\frac{2}{3}} \ \frac{v_1}{v_2} & =\left(\frac{M_1}{M_2}ight)^{2 / 3} \ 	herefore \quad \frac{0.5}{v_2} & =\left(\frac{20 	imes 10^{-3}}{54 	imes 10^{-2}}ight)^{2 / 3} \ \frac{0.5}{v_2} & =\frac{1}{9} \Rightarrow v_2=4.5 \mathrm{~m} / \mathrm{s} \end{aligned}$

An iron sphere of mass $20 \times 10^{-3} \mathrm{~kg}$ falls through a viscous liquid with terminal…

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