A) \[v\]
B) \[v/4\]
C) \[1:4\]
D) \[1:64\]
E) \[30:1\]
Correct Answer: C
Solution :
Terminal velocity of the ball through a viscous medium \[v=\frac{2}{9}\times \frac{g}{\eta }(\rho -\sigma ){{r}^{2}}\] Or \[v=\frac{2}{9}\times \frac{g}{\eta }(\rho ){{r}^{2}}\] Because for viscous medium of negligible density\[(\sigma =0)\] \[\therefore \] \[v=\frac{2}{9}\times \frac{g}{\eta }\times \frac{m}{\frac{4}{3}\pi {{r}^{3}}}\times {{r}^{2}}\] \[\left[ \because \rho =\frac{m}{\frac{4}{3}\pi {{r}^{3}}} \right]\] Or \[v=\frac{2}{9}\times \frac{g}{\eta }\times \frac{m}{\frac{4}{3}\pi r}\] \[\Rightarrow \] \[v\propto \frac{1}{r}\] For the second ball \[v\propto \frac{1}{2r}\] \[\therefore \] \[\frac{v}{v}=\frac{2r}{r}\] Or \[v=\frac{v}{2}\]
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