What is the acceleration due to gravity?

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To determine the acceleration due to gravity on a distant planet, an astronaut measures the time for a transverse pulse to travel a 1.5 m wire with a linear density of 3.1 x 10^-4 kg/m, while a 0.055-kg ball hangs from it. The measured time for the pulse is 0.085 seconds. The mass of the wire is negligible compared to the ball's mass. The discussion seeks an equation for the wave speed in a string, related to its density and tension. Understanding this relationship is essential for calculating the gravitational acceleration.
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Homework Statement



To measure the acceleration due to gravity on a distant planet, an astronaut hangs a 0.055-kg ball from the end of a wire. The wire has a length of 1.5 m and a linear density of 3.1 multiplied by 10-4 kg/m. Using electronic equipment, the astronaut measures the time for a transverse pulse to travel the length of the wire and obtains a value of 0.085 s. The mass of the wire is negligible compared to the mass of the ball. Determine the acceleration due to gravity.

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The Attempt at a Solution


 
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Do you have an equation for the speed of a wave in a string, based on its density and the tension? If not, try http://www.transtutors.com/physics-homework-help/waves/transverse-wave.aspx. (The 3/4 symbols should be equals signs.)
 
The book claims the answer is that all the magnitudes are the same because "the gravitational force on the penguin is the same". I'm having trouble understanding this. I thought the buoyant force was equal to the weight of the fluid displaced. Weight depends on mass which depends on density. Therefore, due to the differing densities the buoyant force will be different in each case? Is this incorrect?

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