A cylindrical hole is bored through a steel block, and a cylindrical piston is machined to fit into the hole. The diameter of the hole is 20.00 ± 0.01 cm, and the diameter of the piston is 19.90 ± 0.02 cm. The clearance is one-half the difference between the diameters. Estimate the clearance and find the uncertainty in the estimate.
What will be an ideal response?
Let X represent the measured diameter of the hole, and let Y represent the measured diameter of the piston. Then X = 20.00, Y = 19.90, 
= 0.01. and 
= 0.02. The clearance is 0.5X — 0.5Y = 0.05 cm.
The uncertainty is 
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