A) \[8\,m{{s}^{-1}}\]
B) \[16\,m{{s}^{-1}}\]
C) \[24\,m{{s}^{-1}}\]
D) \[32\,m{{s}^{-1}}\]
Correct Answer: C
Solution :
Volume of big drop \[=64\times \] volume of a small drop \[\Rightarrow \] \[\frac{4}{3}\pi {{R}^{3}}=64\times \frac{4}{3}\pi {{r}^{3}}\Rightarrow R=4r\] The terminal velocity of spherical rain drop \[v=\frac{2{{r}^{2}}(\rho -\sigma )}{9\eta }\Rightarrow v\propto {{r}^{2}}\] \[\Rightarrow \] \[\frac{{{v}_{1}}}{{{v}_{2}}}={{\left( \frac{r}{R} \right)}^{2}}={{\left( \frac{1}{4} \right)}^{2}}=\frac{1}{16}\] \[\therefore \] \[{{v}_{2}}=16{{v}_{1}}=16\times 1.5=24\,m{{s}^{-1}}\]
You need to login to perform this action.
You will be redirected in
3 sec
