Question

Stoke's Law suggests that velocity of fall of particles is directly proportional to the

• A. Density of the medium
• B. Square of the density of the medium
• C. Radius of the particle
• D. Square of the radius of the particle

Hint:

Stoke's Law: \(v = \frac{2}{9} \frac{r^2 (\rho_p - \rho_f) g}{\eta}\).
- \(v \propto r^2\).
- \(v \propto (\rho_p - \rho_f)\).
- \(v \propto 1/\eta\).

Answer 1

The Correct Option is D

Step 1: Understanding the Question:
This question tests knowledge of Stoke's Law for particle settling.

Step 2: Key Formula or Approach:
Stoke's Law:
\[ v = \frac{2}{9} \frac{r^2 (\rho_p - \rho_f) g}{\eta} \] where \(v\) is settling velocity, \(r\) is particle radius, \(\rho_p\) is particle density, \(\rho_f\) is fluid density, \(\eta\) is viscosity.

Step 3: Detailed Explanation:
According to Stoke's Law, the settling velocity is directly proportional to the square of the radius of the particle (D).
It is also directly proportional to the density difference between the particle and the medium.
It is inversely proportional to the viscosity of the medium.
Other options:
- Density of the medium (A): Inversely proportional.
- Square of the density of the medium (B): Not correct.
- Radius of the particle (C): Velocity is proportional to \(r^2\), not \(r\).
Thus, velocity is proportional to the square of the radius.
Final Answer:
Thus, the velocity is directly proportional to the square of the radius of the particle, which corresponds to option (D).
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