A cylindrical laboratory hydrometer floats vertically in an organic solvent. The length of the hydrometer submerged below the liquid surface is 18 cm18\text{ cm}18 cm.
The hydrostatic pressure exerted by the solvent alone on the flat bottom of the hydrometer is 1.45×103 Pa1.45 \times 10^3\text{ Pa}1.45×103 Pa. Calculate the density ρ\rhoρ of the solvent, giving your answer to 2 significant figures. (Use g=9.81 m s−2g = 9.81\text{ m s}^{-2}g=9.81 m s−2)
The hydrometer is depressed slightly into the solvent and then released so that it oscillates vertically with free simple harmonic motion at a frequency of 1.5 Hz1.5\text{ Hz}1.5 Hz. At t=0 st = 0\text{ s}t=0 s, the hydrometer is released from its maximum displacement of 2.5 cm2.5\text{ cm}2.5 cm.
Calculate the displacement xxx (in cm\text{cm}cm) of the hydrometer at time t=0.40 st = 0.40\text{ s}t=0.40 s.
Calculate the maximum speed of the oscillating hydrometer (in m s−1\text{m s}^{-1}m s−1) to 2 significant figures.
State the effect of depressing the hydrometer further down before release on its: (1) amplitude, (2) period.
