Calculating the Relative Error & Improving Accuracy of Measurements

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To calculate the relative error for the two rod measurements, divide the uncertainty by the measured value for each rod. For Length 1, the relative error is 1x10^-3 / 2.000, and for Length 2, it is 1x10^-3 / 0.100. Length 2 has a higher relative error, indicating it is less accurate than Length 1. To improve the accuracy of Length 2, one could use a more precise measuring instrument or take multiple measurements and average the results. Accurate measurements are crucial for reliable data analysis in scientific experiments.
usamahashimi
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Hi
Can anyone help me to solve the following question;
Q: You measure the length of two rods using a meter ruler and find;
Length 1 = [2.000+/-1x10-3] meter
Length 2 = [0.100+/-1x10-3] meter
find the relative error (fractional error), which value is more accurate? How can we improve the accuracy of the least accurate reading?
Note: in both equations the +/- is written above and below of each other without the '/' sign.

Thanks.
 
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Thanks
Matt
 
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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