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NEET Sample Paper NEET Sample Test Paper-44

  • question_answer
    A metallic sphere of mass M falls through glycerine with a terminal velocity v. If the we drop a ball of mass 8M of same metal into a column of glycerine, the terminal velocity of the ball will be:

    A) 2v        

    B) 4v      

    C) 8v                    

    D) 16v

    Correct Answer: B

    Solution :

    Terminal velocity \[\left( {{V}_{T}} \right)=\frac{2}{9}\frac{\left[ \rho -\sigma  \right]{{r}^{2}}}{\eta }\] \[\operatorname{Mass} of sphere m = \frac{4}{3} \pi {{r}^{3}}\rho \] \[\operatorname{m}\propto {{r}^{3}}\] \[\frac{{{r}_{1}}}{{{r}_{2}}}={{\left( \frac{{{m}_{1}}}{{{m}_{2}}} \right)}^{{}^{1}/{}_{3}}}={{\left( \frac{m}{8m} \right)}^{{}^{1}/{}_{3}}}\] Use this result to calculate ratio of terinal velocity \[\frac{{{V}_{{{T}_{1}}}}}{{{V}_{{{T}_{2}}}}}=\frac{{{r}^{2}}_{1}}{{{r}^{2}}_{2}}=\frac{1}{4}\] \[{{\operatorname{V}}_{{{T}_{2}}}}=4V\]


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