Sedimentation rate becomes zero when the density of the particle equals that of the surrounding medium, making option 3 correct. This fundamental principle from Stokes’ law governs particle behavior in centrifugation and sedimentation analysis.

Introduction

The sedimentation rate of a particle determines how quickly it settles under gravitational or centrifugal force, crucial in biochemistry techniques like ultracentrifugation. This question tests understanding of density-dependent buoyancy, where equal densities prevent net movement. Life sciences students encounter this in cell biology and analytical techniques for protein or organelle separation.

Option Analysis

Each option tests density relationships affecting buoyant force versus gravitational force.

• Density of particle < surrounding medium
  The particle experiences upward buoyancy greater than its weight, causing it to float or rise (negative sedimentation), not settle.

• Density of particle > surrounding medium
  Gravitational force exceeds buoyancy, resulting in positive sedimentation as the particle sinks at a measurable rate.​

• Density of particle = surrounding medium
  Buoyant force exactly balances gravitational force (Archimedes’ principle), yielding zero net force and thus zero sedimentation rate; the particle remains suspended.​

• Density of particle = twice surrounding medium
  Twice the density creates strong downward force, producing high sedimentation velocity proportional to the density difference.

Stokes’ Law Mechanism

Sedimentation velocity v=2r2(ρp−ρm)g9ηv=9η2r2(ρp−ρm)g, where $r$ is particle radius, ρpρp and ρmρm are particle and medium densities, $g$ is gravitational/centrifugal acceleration, and $\eta$ is viscosity. The term (ρp−ρm)=0(ρp−ρm)=0 directly makes $v=0$, independent of size or field strength.

In centrifugation, this equilibrium occurs rapidly, with frictional drag balancing any residual motion.​

Applications in Life Sciences

This principle enables density gradient centrifugation (e.g., sucrose gradients) for isolating organelles, viruses, or ribosomes at their isopycnic points. In analytical ultracentrifugation, sedimentation coefficients (s=vω2rs=ω2rv) help determine molecular weights when densities match.​

Exam Strategy

Focus on the (ρp−ρm)(ρp−ρm) term in Stokes’ equation for similar questions in GATE/CSIR-NET biochemistry. Visualize: equal densities = neutral buoyancy like fish in water.​