A) 80 cm/s
B) 40 m/s
C) 10 cm/s
D) 5 cm/s
Correct Answer: D
Solution :
Since, ball is moving with a constant speed v, there is no acceleration in it, the net force acting on it, must be zero. That is, \[6\pi \eta rv=\frac{4}{3}\pi {{r}^{3}}(\rho -\sigma )g\] \[\Rightarrow \] \[v=\frac{2}{9}\frac{{{r}^{2}}(\rho -\sigma )g}{\eta }\] \[\Rightarrow \] \[v\propto {{r}^{2}}\] Here, \[{{v}_{1}}=20\,cm/s.\]\[{{r}_{1}}=2\,cm,\]\[{{r}_{2}}=1\,cm\] \[\therefore \] \[\frac{{{v}_{1}}}{{{v}_{2}}}=\frac{20}{{{v}_{2}}}=\frac{{{(2)}^{2}}}{{{(1)}^{2}}}\]
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