Question

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 20.04 ± 0.01 cm, and the diameter of the piston is 19.92 ± 0.04 cm. The clearance is one-half the difference between the diameters. Estimate the clearance and find the uncertainty in the estimate.

Answer 1

Answer:

The diameter of the hole is 20.04 ± 0.01 cm

The diameter of the piston is 19.92 ± 0.04 cm.

We are given that The clearance is one-half the difference between the diameters.

So, Clearance = $\frac{1}{2}(20.04-19.92)$

                      = $0.06$

Uncertainty in the estimate =  $\frac{1}{2}(0.01+0.04)$

                                              =  $0.025$

So, Clearance with uncertainty is $0.06\pm 0.025$

Hence  the clearance is 0.06 and the uncertainty in the estimate. is 0.025