Describe a way to measure not calculate the circumference of

Describe a way to measure (not calculate) the circumference of a cylinder to the nearest 0.1 mm using only a nonflexible ruler graduated in millimeters. Do not use the formulae C=2*(pi)*radius or C= pi*diameter; measure the circumference directly. Also note that the required measurement uncertainty is 0.1 mm while the ruler itself is graduated in whole millimeters and has a reading error of 0.5 mm (five times larger than requested). Think of a way to reduce the uncertainty.

Solution

One way to do this experiment is

i) Mark a position on the rim of the cylinder. Place the cylinder over the ruler. Mark the initial measure on the ruler at that point where the mark touches on the ruler. Roll the cylinder over the ruler. When the cylinder completes one full rotation, take a reading on the mark against the ruler.

But this procedure involves a finite value of error, which can be reduced by taking multiple data - such as instead of one reading or taking reading over one full rotation, perform the procedure for lets say, 20 rotation and then average over 20 to get the approximate value of circumference of the cylinder.

ii) One more addition to this way of performing the experiment is to have the mark replaced with a strip of 0.5 mm thickness and having least count 0.1 mm (i.e., 6 sub-divisions (0 inclusive)). So before rolling the cylinder, the \'0\' mark on the strip coincide with an initial reading on the ruler, after the roll-over the accurate reading can now be taken down to 0.1 mm. This should reduce the uncertainity.