The terminal velocity of a copper ball of radius $5 \mathrm{~mm}$ falling through a tank of oil at room…

The terminal velocity of a copper ball of radius $5 \mathrm{~mm}$ falling through a tank of oil at room temperature is $10 \mathrm{~cm} \mathrm{~s}^{-1}$. If the viscosity of oil at room temperature is $0.9 \mathrm{~kg} \mathrm{~m}^{-1} \mathrm{~s}^{-1}$, the viscous drag force is:
  1. $8.48 \times 10^{-3} \mathrm{~N}$
  2. $8.48 \times 10^{-5} \mathrm{~N}$
  3. $4.23 \times 10^{-3} \mathrm{~N}$
  4. $4.23 \times 10^{-6} \mathrm{~N}$

Solution

By Stroke's law, $\mathrm{F}=6 \pi \eta r v$ (where, the symbols have their usual meanings) $\begin{aligned} \mathrm{F} & =6 \times 3.14 \times 0.9 \times 5 \times 10^{-3} \times 10 \times 10^{-2} \\ \mathrm{~F} & =84.78 \times 10^{-4} \\ & =8.478 \times 10^{-3} \mathrm{~N}=8.48 \times 10^{-3} \mathrm{~N} \end{aligned}$ .

Asked in: NEET 2022 (Phase 2)

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