Explanation

Terminal velocity of a small sphere moving through a viscous fluid is given by Stokes’ law:

$$ v = \frac{2}{9}\frac{r^2 g (\rho_s - \rho_f)}{\eta} $$

Diameter of sphere:

$$ d = 2\,mm = 0.2\,cm $$

Radius:

$$ r = 0.1\,cm $$

Density of sphere:

$$ \rho_s = 10.5\,g/cm^3 $$

Density of glycerine:

$$ \rho_f = 1.5\,g/cm^3 $$

Viscosity of glycerine:

$$ \eta = 10\ \text{Poise} $$

Acceleration due to gravity:

$$ g = 10\,m/s^2 = 1000\,cm/s^2 $$

Substituting all values:

$$ v = \frac{2}{9}\times\frac{(0.1)^2 \times 1000 \times (10.5 - 1.5)}{10} $$

$$ v = \frac{2}{9}\times\frac{0.01 \times 1000 \times 9}{10} $$

$$ v = \frac{2}{9}\times 9 $$

$$ v = 2\,cm/s $$

Final Answer: $$ \boxed{2.0\ \text{cm/s}} $$

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