A solid sphere, of radius R acquires a terminal velocity \upsilon _{1} when falling (due to gravity ) through a viscous fluid having a coefficient of viscosity \eta. The sphere is broken into 27 identical solid spheres. If each of these spheres acquires a terminal velocity, \upsilon _{2}, when falling through the same fluid, the ratio (\upsilon _{1}/\upsilon _{2}) equals :

 

  • Option 1)

    9

  • Option 2)

    1/27

  • Option 3)

    1/9

  • Option 4)

    27

 

Answers (1)

M=\rho \times \frac{4}{3}\pi R^{3}

\frac{M}{27}=\rho \times \frac{4}{3}\pi r^{3}

r\rightarrow \frac{R}{3}

V_{T}\alpha (Radius)^{2}

\frac{V_{T}}{V_{new}}=\frac{R^{2}}{(R/3)^{2}}=9


Option 1)

9

Option 2)

1/27

Option 3)

1/9

Option 4)

27

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