The correct answer is A. 213.5 cm/sec.
The settlement velocity of a solid is the velocity at which it settles in a fluid. It is calculated using the Stokes equation:
$$v_s = \frac{2}{9} \frac{\mu g d^2}{\rho_s – \rho_f}$$
where:
- $v_s$ is the settlement velocity
- $\mu$ is the viscosity of the fluid
- $g$ is the acceleration due to gravity
- $d$ is the diameter of the solid
- $\rho_s$ is the density of the solid
- $\rho_f$ is the density of the fluid
In this case, the viscosity of water at 10°C is 1.002 x 10^-3 Pa s, the acceleration due to gravity is 9.81 m/s^2, the diameter of the solid is 0.5 mm, the density of the solid is 1.75 g/cm^3, and the density of water is 0.998 g/cm^3. Substituting these values into the Stokes equation gives:
$$v_s = \frac{2}{9} \frac{1.002 \times 10^{-3} \times 9.81 \times (0.5 \times 10^{-3})^2}{1.75 – 0.998} = 213.5 \text{ cm/sec}$$
Therefore, the settlement velocity of the solid is 213.5 cm/sec.
Option B is incorrect because it is the settling velocity of a solid with a diameter of 1 mm. Option C is incorrect because it is the settling velocity of a solid with a diameter of 2 mm. Option D is incorrect because it is the settling velocity of a solid with a diameter of 5 mm.