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

  • question_answer
    A marble of mass \[x\] and diameter 2r is gently released in a tall cylinder containing honey. If the marble displaces mass y (< \[x\]) of the liquid, then the terminal velocity is proportional to

    A) \[x+y\]

    B) \[x-y\]

    C) \[\frac{x+y}{r}\]          

    D) \[\frac{x-y}{r}\]

    Correct Answer: D

    Solution :

    [d] \[{{v}_{0}}=\frac{2}{9}\frac{{{r}^{2}}(\rho -\rho ')g}{\eta }\] \[Now,\text{ }x=\frac{4}{3}\pi {{r}^{3}}\rho \,\,or\text{ }\rho \propto \frac{x}{{{r}^{3}}}\] \[Similarly,\text{ }\rho '\propto \frac{y}{{{r}^{3}}}\] \[\therefore {{v}_{0}}\propto \frac{x-y}{r}\]


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