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A solid spherical bead of lead (uniform density= $11000 \; kg/m^{3}$) of diameter $d = 0.1\; mm$ sinks with a constant velocity $V$ in a large stagnant pool of a liquid (dynamic viscosity = $1.1 \times 10^{-3}\; kg \cdot m^{-1} \cdot s^{-1}$). The coefficient of drag is given by  $C_{D} = \frac{24}{Re}$, where the Reynolds number (Re) is defined on the basis of the diameter of the bead. The drag force acting on the bead is expressed as $D = \left ( C_{D} \right )\left ( 0.5 \rho V^{2}\right ) \left ( \dfrac{\pi d^{2}}{4} \right )$, where $\rho$ is the density of the liquid. Neglect the buoyancy force. Using $g = 10 \;m/s^{2}$, the velocity $V$ is ____________ $m/s$.

  1. $\frac{1}{24}$
  2. $\frac{1}{6}$
  3. $\frac{1}{18}$
  4. $\frac{1}{12}$
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