A) \[\text{1}.0\times \text{1}{{0}^{-\text{4}}}\text{ m}/\text{s}\]
B) \[2.0\times \text{1}{{0}^{-\text{4}}}\text{ m}/\text{s}\]
C) \[2.5\times \text{1}{{0}^{-\text{4}}}\text{ m}/\text{s}\]
D) \[5.0\times \text{1}{{0}^{-\text{4}}}\text{ m}/\text{s}\]
Correct Answer: C
Solution :
Radius r = 0.0015 mm \[=15\times {{10}^{-7}}m\] Coefficient of viscosity \[=2.0\times {{10}^{-5}}kg/ms\] Density of water \[=1\times {{10}^{3}}kgm/{{m}^{3}}\] Terminal velocity \[v=\frac{2}{9}\frac{{{r}^{2}}\rho g}{\eta }\] \[v=\frac{2}{9}\times \frac{{{(15\times {{10}^{-7}})}^{2}}\times 1\times {{10}^{3}}\times 10}{2\times {{10}^{-5}}}\] \[v=2.5\times {{10}^{-4}}m/s\] Note : - (The density of water\[=\text{1}.0\times \text{1}{{0}^{\text{3}}}\text{kg}/{{\text{m}}^{\text{3}}}\text{and}\,\text{g}=\text{1}0\text{m}/{{\text{s}}^{\text{2}}}\])
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