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.

Group of answer choices

T proportional to $($liquid$)1/2$

T proportional to $($liquid$)2$

T proportional to $($liquid$)1/2$

T proportional to $($liquid$)2$

T proportional to $($liquid$)$