JEE Main & Advanced Physics Fluid Mechanics, Surface Tension & Viscosity / द्रव यांत्रिकी, भूतल तनाव और चिपचिपापन Question Bank Self Evaluation Test - Mechanical Properties of Fluids

  • question_answer
    If a ball of steel (density\[\rho =7.8g\,c{{m}^{-3}}\]) attains a terminal velocity of \[10cm{{s}^{-1}}\] when falling in a tank of water (coefficient of viscosity \[{{\eta }_{water}}=8.5\times {{10}^{-4}}Pa-s\]) then its terminal velocity in glycerin(\[\rho =12gc{{m}^{-3}},\,\eta =13.2Pa-s\]) would be nearly

    A) \[1.6\times {{10}^{-5}}cm{{s}^{-1}}\]

    B) \[6.25\times {{10}^{-4}}cm{{s}^{-1}}\]

    C) \[6.45\times {{10}^{-4}}cm{{s}^{-1}}\]

    D) \[1.5\times {{10}^{-5}}cm{{s}^{-1}}\]

    Correct Answer: B

    Solution :

    [b] \[v\propto \frac{\rho -{{\rho }_{0}}}{\eta }\] \[\therefore \,\,\,\frac{{{v}_{2}}}{{{v}_{1}}}=\frac{\rho -{{\rho }_{02}}}{\rho -{{\rho }_{01}}}\times \frac{{{\eta }_{1}}}{{{\eta }_{2}}}=\frac{7.8-1.2}{7.8-1}\times \frac{8.5\times {{10}^{-4}}\times 10}{13.2}\] \[=6.25\times {{10}^{-4}}cm{{s}^{-1}}\]


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