Chapter 12, Problem 12RQ

1. 12. When a buoyant cylinder of height H, such as a fishing cork, is placed in a liquid and the top is depressed and released, it will bob up and down with a period T. We can conduct a series of tests and see that as the height of the cylinder increases, the period of oscillation also increases. A less dense cylinder will have a shorter period than a denser cylinder, assuming of course all the cylinders will float. A simple expression for the period is:

   $T=2\pi \sqrt{\frac{{\rho }_{cylinde{r}^H}}{{\rho }_{liquid}g}}$

where g is the acceleration due to gravity, ρ_cylinder is the density of the material, and ρ_1iquid is the density of the fluid. By testing cylinders of differing heights, we wish to develop a model for the oscillation period, shown in the following graph.

1. a. What are the units of the coefficient (0.1 04) shown in the model?
2. b. What is the oscillation period in units of seconds of a cylinder that is 4 inches tall?
3. c. If the oscillation period is 0.2 seconds, what is the height of the cylinder in units of inches?
4. d. We will conduct a series of tests with a new plastic (polystretchypropylene) that has a specific gravity of 0.6. What is the specific gravity of the fluid?