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.
Step 1 of 1:
In this question, we are asked to estimate the clearance and find the uncertainty in the estimate.
Let assume is the diameter of hole =
And is the diameter of the piston =
The clearance is one-half the difference between diameters.
Hence estimate of clearance =
Hence the estimate of clearance is .
Uncertainty in the estimate:
If are independent measurements and are constants, then
Uncertainty in the measurement …(1)
uncertainty in the diameter of hole =
uncertainty in the diameter of the piston =
Hence uncertainty in the estimate is .
We can therefore express the clearance