A thin test tube is partially filled with lead pellets so that it floats vertically in a fluid.Use Archimedes' Principle to calculate that if displaced slightly from its equilibrium position the test tube will undergo SHM in the vertical direction and derive how the time period is related to the density of the fluid. A)T proportional to $\rho$(liquid) B)T proportional to $\rho$(liquid)^1/2 C)T proportional to $\rho$(liquid)² D)T proportional to $\rho$(liquid)^-2 E)T proportional to $\rho$(liquid)^-1/2

Question

Quizplus · Accepted Answer

The time period (T) of the simple harmonic motion (SHM) of the test tube in the fluid is related to the density of the fluid ($\rho$) because the buoyant force, which is dependent on the density of the fluid, provides the restoring force necessary for SHM. The correct relationship involves the square root of the inverse of the fluid density, indicating that as the density of the fluid increases, the time period of the oscillation decreases. This is consistent with the principles of buoyancy and SHM, where the restoring force is directly related to the displacement from equilibrium, and the density of the fluid affects the magnitude of this restoring force.

A Thin Test Tube Is Partially Filled with Lead Pellets ρ\rhoρ

A Thin Test Tube Is Partially Filled with Lead Pellets $\rho$