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WB JEE Medical WB JEE Medical Solved Paper-2006

  • question_answer
    Sixty four spherical rain drops of equal size  are falling vertically through air with a terminal velocity \[1.5\,\text{m}{{\text{s}}^{-1}}.\] If these drops coalesce to form a big spherical drop, then terminal velocity of big drop is :

    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 smalldrop \[\Rightarrow \]               \[\frac{4}{3}\pi {{R}^{3}}=64\times \frac{4}{3}\pi {{r}^{3}}\] \[\Rightarrow \]               \[R=4r\] The terminal velocity of spherical rain drop \[v=\frac{2{{r}^{2}}(\rho -\sigma )}{9\eta }\]                 \[\Rightarrow \]               \[v\propto {{r}^{2}}\] \[\Rightarrow \]               \[\frac{{{v}_{1}}}{{{v}_{2}}}={{\left( \frac{r}{R} \right)}^{2}}={{\left( \frac{1}{4} \right)}^{2}}=\frac{1}{16}\] \[\therefore \]  \[{{v}_{12}}=16\,{{v}_{1}}=16\times 1.5=24\,m{{s}^{-1}}\]


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