Your vessel has a displacement of 10,000 tons. It is 350 feet long and has a beam of 55 feet. You have timed its rolling period to be 15.0 seconds. What is your vessel's approximate GM?
• Formula for rolling period and metacentric height GM for a ship • Unit consistency: converting seconds, feet, and using the correct constant • How long rolling period relates to small GM (stiff vs tender ship)
• Write down the standard empirical formula that relates rolling period (T), beam (B), and GM. Which variables do you already know from the question? • Before plugging in numbers, think: does a longer rolling period correspond to a larger or smaller GM? Use that to eliminate at least one or two options. • After you compute GM, compare the result to the beam (55 ft). Does the GM value make physical sense for a ship of this size?
• Be sure you are using the correct rolling-period formula for large ships, not small boats or models. • Check that you are squaring the correct variable (is it T or B in the numerator/denominator?) • After calculating, verify that the magnitude of GM (on the order of a few feet) is reasonable for a 350-ft ship and that your answer matches one of the choices.
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