A) \[\frac{2}{9}{{r}^{2}}\left( \frac{1-\rho }{\eta } \right)\,g\]
B) \[\frac{2}{81}{{r}^{2}}\left( \frac{\rho -1}{\eta } \right)\,g\]
C) \[\frac{2}{81}{{r}^{4}}{{\left( \frac{\rho -1}{\eta } \right)}^{2}}g\]
D) \[\frac{2}{9}{{r}^{4}}{{\left( \frac{\rho -1}{\eta } \right)}^{2}}g\]
Correct Answer: C
Solution :
Velocity of ball when it strikes the water surface \[v=\sqrt{2gh}\] ?(i) Terminal velocity of ball inside the water \[v=\frac{2}{9}{{r}^{2}}g\frac{\left( \rho -1 \right)}{\eta }\] ?(ii) Equating (i) and (ii) we get \[\sqrt{2gh}=\frac{2}{9}\frac{{{r}^{2}}g}{\eta }(\rho -1)\] Þ \[h=\frac{2}{81}{{r}^{4}}{{\left( \frac{\rho -1}{\eta } \right)}^{2}}g\]
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